Okay, so Arena mode is pretty much the best mode to play in TF2 in my opinion. I have played it alot, and I consider myself good at it, so why not make a guide about it. This is my first attempt at making anything like this so be gentle on me. :D

So in Arena, you are thrown in a map with varying amounts of players (usually max. amount is 12 per team) set with two objectives. Killing the opposing team, or capturing the control point.
Arena maps feature a limited amount health and ammo pickups, while some maps don't have health pickups at all, which makes Engineers (and their dispensers) and Medics even more valuable. Also, the first kill of the round gains the killer a few seconds of full darn crits which makes it that much more worthy to try and rush in for that sweet sweet first blood. But this can be also triggered by Dead Ringer Spies, and when that happens the Announcer will give no warnings at all, so be careful at the start of the match.
All maps also have a capture point that you can capture after a set amount of time. Capturing the point will win you the round no matter what the situation. Some (or even most) people consider this cowardly and annoying, but to me it just makes sense. No one wants to chase a team of Spies around and waste time and eventually get killed. The same also applies to Engineer nests.
The way to achieve this can be difficult and complicated though. But everything starts from the teams themselves, so let's move onto that segment, shall we?

In Arena, your teams -as always- should be diverse, while focusing to pick the other teams Medic, and protect your own one. You should have a mix of long and short range classes. Snipers and Spies really shine in this game mode almost as much as the Medic, since they are the best at picking lone roamers.

You should accompany the Medic with a few combat classes such as the Heavy, Soldier and Demoman. In a 4v4 match, the team with a similar composition of different range classes will be more likely to win. Although a team of Scouts can be devastating against a team dependant on a Medic.
Being a combat Engineer is also a very viable thing in Arena, especially if the other team has no Medic. While most people frown upon this, it is rather easy to take down a combat Engy with a Medic-Soldier/Demo/Heavy/Pyro combo. Basicly any class with a Medic.
Now, I do understand most of the time Arena is played in public servers so it's hard to get this kind of composition. But you can always try to nudge your team in the right direction.
I'll be leaving this section short as this isn't as likely to influence people playing Arena.

Btw, a full 12 player team full of these wins every match--->

In Arena mode, it is usually best to stick together with the Medic and other teammates while having one or two people flanking the other Team. This is the standard tactic because it works.
Nuff said.Let's say it's a 6v6 match in Granary. Both teams have the same class composition, but the BLU team sends a Scout from the other side to pick the enemy Medic, while the rest of the BLU team are defending their own. While the RED team is focusing on harassing the Medic, the BLU Scout sneaks in and takes out the RED Medic. After this he retreats to the safety of their team's Medic and other teammates and happily takes out the unhealed RED team.

The classes you should have flanking are Scout,Soldier,Demoman and Spy, since they can deal lots of damage quickly. A Pyro can work as well, but can be detected before getting into lethal range.

Strategies can change drastically because skill is a HUGE factor in Arena.
I hope you will pick the basics from this guide and make one of your own strategies with your friends! Does someone like rocketjumping and someone likes being a Medic? Be an unstoppable Soldier/Quickfix Medic combo that can reach any place quickly!
Someone likes to play Fatscout and someone mains Pyro? Give the Fatscout the protection he needs by airblasting stray rockets and nades away, while the Fatscout takes care of those pesky Scouts.

The possibilities are endless! (Actually they're not, but there are many!)
I'll be detailing class specific strategies later on. The chapters about them will hopefully be short and sweet for your convinience.

Now for me, it seems kinda odd making a whole segment of this guide about capturing, seeing how many people despise it or just don't want to do it. But, here I'll try to give you some tips on how, when, and why to capture the point instead of killing the other team.

"Why?" You're the only one alive in your team, and you are searching for the last 2 remaining enemies. After a brief search, you see no one. Chances are, they are both Spies. Now, you don't want to chase them around when they'll just trickstab you or headshot you with the Ambassador while roaming freely. This is where capping comes in. You walk to the capture point, and everyone hears the capturing sound and sees the capturing cues on the HUD. Now the enemy Spies have to confront you. They get out of their hideyholes, and start strolling over to the point. Once they reach the point, it is already half capped, giving you even more of an edge, when the pressure stacks on the Spies. When you're capping remember to keep spinning in erratical circles to keep an eye on every possible direction the enemy can come from. Once you see the enemy, you can use the possible cover the point can provide to hide yourself from those nasty Amby Spies. At this point the point is capped and the only thing to do is bash those Spies' face in with your melee.

Now that I think of that, it covers a bit of all the 3 categories I was going to explain. xD But let's cover the remaining two shortly anyway.

"When?" Well, generally when you can't find your opponent and it is unpractical to go chasing them.
Also, when you have alot of people nearby the point with you, you can hint them to capture with you. Now this is a great trick to defeat Medic-Solly/Demo/Heavy combos. Just get your group up and capture the point before the combo can kill you. Works even better with a good Pyro! (This is a very rare occurance, since the point becomes active only after a set amount of time)

"How?" Silly question, I know. Just stand on the point, yeh? Good. But seriously though, keep checking every possible entrance and listen for rocket jump sounds or anything else that hints an incoming attack. Use the possible cover, such as the "shields" in Nucleus or containers in Granary.
You'll be the king of points in no time!

In my opinion, capping is a part of the game mode and a completely viable method of winning, and you should not be discouraged to do so by others.

This will hopefully be a really big chapter in the future, because this is THE chapter that you can participate in. If you know something not mentioned in this guide, share it in the comments and get it featured here permanently with your name and with a personalized thanks from me!

- Use those flappy things on the sides of your head and listen to your surroundings! Do you hear your teammates exploding? Chances are there are Soldiers and Demos. You heard a fast double shotgun shot? Be aware of the FaN Scout flanking you! The list goes on and on. Now it's up to you to start to actually listen what's happening around you!

- Take a look at the killfeed on the upper right corner. Take a closer look at the kill icons and names. A minigun kill icon? I think it's safe to assume there's a Heavy. A sentry kill? Oh snap boyos, better go get that sentry before it's level 3!

- Did that HUD icon just flash with the opposing teams color? Now you know someone passed trough the central point! Was it x2 capture speed? Maybe a Scout. Maybe. Or it could be a Heavy-Medic combo. Get to high ground and investigate.

- Someone writing too much rethorical questions in a Steam Guide? Get that sucker by writing angry comments at him in the comments section!

- As a Pyro, puff some flames in the air if a Sniper is aiming at you. The flames will hide your head if fired properly. Aim your flamethrower slightly upwards.

- When you know an enemy is low on health, position yourself between the enemy and the health kit. You'll efficiently block his access to health.

- Watch out for Machina's and Wranglers light trace's and use them to track the sentry or Sniper! Remember that Snipers can still move!
A huge thanks to The_Dude for providing this very useful information that I didn't mention!

- If you're being chased by a lone enemy, and you know he's on somewhat low health run around a corner and then wait for them behind it. Then when they arrive surprise them with your melee! Don't try this on full health Heavies or anything that you think can still overpower you.
Thanks, Lord North! I'm sure lots of people will put this tip to good use!

- If you're a Spy, don't let the enemy know you're one! At the start of the round, disguise as a teammate, but different class. They won't expect a Spy and won't ever see the backstab coming!
This very nifty tip was provided by 888888Zombies (拒绝交易). This is hella useful! My gratitude!

How To Play: As a Scout, you can play very aggressively or defensively. This depends on your loadout. Health regenerating items are one of your biggest friends in this game mode. Consider using Mad Milk and/or Candy Cane with a side dish of some Short Stop.
Stay out of tight spots such as the small houses in badlands. You can still pop in there, get a few shots on the enemies and get out. Great for chipping the enemies' health away if they don't have a Medic. If they do, shoot him. Simple. With the Short Stop, you can play it safe and harass pretty much everyone form afar. Just remember to throw your Man Mad Milk at the beefier classes!
With the other primary weapons you can go in more aggressively and get in there to snatch that First Blood buff! Remember that, if you're on low health you can quickly go get that possible health kit and be back twice as bad in no time!

How To Counter: Now this is a tricky thing. In arena, Good scouts are very hard to counter effectively. One thing does stand out from the rest. *cue angelic chorus* The Mini-Sentry! This bad boy with the Pistol can bring those little dodging monstrosities down in no time! Just make sure to take them down before they get to a medikit/Medic.
And a good Heavy can also bring a Scout down with proper ambushing skills. Tomislav helps out alot here.

How to play: Stick to the Medic while searching for high ground. If possible, rocket jump up there, scout for enemies, and rain death on them! It really helps to have the high ground with a rocket launcher that has a lot of splash damage, like the stock, Original and Black Box etc. Speaking of Black Box. This baby here has the massive advantage of +15 health on hit. Needless to say, very helpful if your team has no Medic. Even with a Medic it is one of the best. Many may also favor the Direct Hit. Don't seek high ground as usual. It is way more useful to just lay low and shoot them straight with the Direct Hit.
Also, as a Soldier, remember you can rocket jump to safety if you happen to encounter a Heavy-Medic combo. Alert your team, and take that duo of fat death down together in no time!

How to counter: The best counter would be Pyro. With the stock Flamethrower or the Degreaser you can airblast those nasty rockets right back at the Soldier! But, maybe you're playing on a map where he always gets the high ground advantage? Introducing Scout! If the Soldier has the high ground, face him as a Scout. Utilize the same platform as he does by using your double jump to jump off the platform and back with the double jump.
Demoman also tends to do the trick nicely with the Chargin' Targe on his side. There is one devious trick you can try: When the Soldier shoots you from the skies, crouch jump the same time as the rocket hits the ground. You might just make the jump, and air strafe to the same platform he is on. Works with any class. Kirstu's seal of quarantee!

How to play:This is where some intelligent thinking comes in. Pyro's afterburn is absolutely devastating if the other team doesn't have any reliable source of healing. You rely on ambushing your enemies as always. This time there are limited ways of replenishing health, and you might want to say hello to our little friend Backscratcher. Now this is a bit situational, being useful only in maps that have health pickups. If the map doesn't have any heath pickups, well... It's going to be a bit harder.
You have to use alternate routes and airblast alot in order to maintain a reasonable amount of health. Surprisingly, the Backburner works pretty well, IF you know how to ambush properly. Read a Pyro guide for that. Works really well with the Powerjack. Flare Gun works wonders by chipping an insane amount of health relatively quickly.
Remember that you can airblast people off of cliffs and into pits.

How to counter: I think Sniper works the best here. Just don't stand too still for the Flares to hit you. The stock Sniper Rifle is a good rifle to use against Pyros. Huntsman can do well as well, but you might get killed by your own arrow if fired against a good Pyro.
Scout can also outmanouver Pyros by kiting them. (Keeping the same distance from the Pyro. Refer to a Scout guide or TF2 Wiki for more information) Shortsop does really good job, as you can keep a safe distance from the Pyro's flamethrower. Mad Milk does a good job at extinguishing yourself.

How to play: Look out for ammo, as Demomen have a very limited amount of ammo for their primary weapons. Be careful with Scouts as they are your direct counter. Stick with other teammates so you can't be picked so easily with a Scout. Also, sticky bombs work moderately well against Scouts, providing you can trap them.
Consider using the Persian Persuader with one of the shields. The health from other peoples weapons and ammo packs will come in handy. Chargin' Targe works insanely well preventing that pesky afterburn from Pyros!

How to counter: Pick. Scout. Nuff said. Seriously, a Scout should be able to pick a Demoman easily no matter the situation. (Unless the Demoman is using Loch-N-Load which can insta-gib a Scout (I'm looking at you Highway)) If you're having trouble with Demomen, try using a different primary other than the Shortstop. The insane close range burst damage that the other primaries possess can make it a lot easier.
Combat Engineer with a Pistol and Sniper also work fine.

How to play: Stick into tight and small places where you can surprise your enemies. Remember to jump around corners while revving your minigun. If you like moving around alot, you have two choices; Gloves Of Running Urgently and Fists Of Steel. The GRU allows you to move faster, but take more damage, while the FoS allow you to move more safely. Just watch out for Spies and Snipers.
Tomislav works really well at ambushing in these places. Sandvich is also a lifesaver! You can also try a tactic called Fatscouting which involves using only your shotgun and melee. (Which I have a liking for. It's awesome!)

How to counter: Sniper, Spy, the usuals. Anything really, if he is alone. If accompanied by a Medic, remember to get the Medic first! Also, Solly with a Direct hit works as well.
And for Talos's sake, stay the firetruck away from him! Distance is your best friend against a Heavy. Capping is very effective against a Heavy, since it takes a long time for him to reach the point. Just don't let him ambush you.

How to play: You pretty much have 2 ways to go: Use Gunslinger, or any other wrench. Talking about the latter first. Build a lvl 2 sentry ASAP near your base and a dispenser for your teammates' leisure. If you manage to do this and keep most of your team alive, you've pretty much won. You should also try to haul the sentry closer to the middle after a while. The Eureka Effect helps if you are in a map, where there are less ammo pickups. But bear in mind, that you have to build it in a place where it will be useful later in the round, since you can't haul your buildings!
Okays, then the Gunslinger. First of all, yes I know, this thing is considered the cancer of Arena, but it can be easily countered. With your extra health you can afford to be a bit more aggressive. Pistol with Widowmaker/Frontier Justice is encouraged. Hide your minisentry to places where it can catch people off guard, like in a bush or a corner. Also, you can place one near the possible medikit (or even right on it) to finish off low health enemies looking for some badly needed heals.
Huddle around your sentry and deal devastating damage with your combined sentry-Pistol damage. Remember that it is just a building and meant to be destroyed and you can quickly build another one. Remember to hide a Dispenser for your team as well!

How to counter: Medic/(Insert any class) will work absolutely best. The minisentry will do minimal damage and get you practically free Übercharge. Just remember to watch your surroundings as one of the missions of a minisentry is to distract people while allowing other classes to ambush them. The same also applies against Engineers using any other melee weapon than Gunslinger.
And of course, how could I not mention him. The Spy. Works amazingly well, though not as well as the Medic-(insert class), in my opinion. If the Engineer is using the Gunslinger, use the Red Tape Recorder! As most Engineers abandon the minisentry instead of removing the sapper, you gain more time to kill the Engineer while he is unable to build another sentry, because it's still being sapped!
Depending on the sentry's location, Sniper can also work extremely well. If the sentry is in an open location, feel free to spam it and the Engineer near it!

How to play: This one's a toughie. Okays. Remember to heal everyone! Healing is im-por-tant! Comprendo? Capische? If a teammate walks up to you with missing health, you check if he's one of your own, and then heal/overheal him if you have time. No matter the class. They will thank you. (No quarantee) Also, stay alive.
Watch out for Sollies in the sky, Spies behind you etc. You can be facing any direction while healing your patient, so be on the lookout. Don't lose your patient!
Lets talk about some weapons. If you're looking for a bit more excitement, pick Blutsauger and assist your patient at killing. Overdose works great as well. As for the Mediguns, Quick-Fix and Vaccinator work wonders because of their fast-charging Übercharges. (See the connection with Overdose?) Solemn Vow will be helpful to tell people if enemies are worth chasing after. Übersaw works as well by giving you that yummy Übercharge. Don't get too risky with it, though.

How to counter: Well now. How do you counter a Medic? Usually he'll be with teammates. It depends. Usually the best way is not so dependant on classes, but strategy. Distraction. You need to catch the Medic's patient off guard, and while he's busy with spamming your teammates, someone should swoop in, kill the MeeM, and possibly kill the patient if he hasn't noticed you. Being a Scout or a Spy helps alot when ambushing.
The next part is a bit controversial, but remember how Medic countered the Combat Engineer? Well, he counters Medic as well, by providing the best distraction against the Medic/sumting combo. Doesn't work quite as well against experienced Medics, though. Trust me, a good dodging and aware Medic is the worst thing evurr!!

How to play: Firstly, you need to be prepared for everything, which is why I wholeheartedly recommend the SMG and stock Sniper Rifle. Altough with proper practice, Huntsman makes for an excellent weapon. Melee is a matter of personal taste, but Tribalman's Shiv can do wonders with the bleed damage.
Every map has some good sniping spots, so you should always aim to get the first blood in order to snatch some of those pro players early on. But there are lots of "unknown" sniping spots. You should try to roam and move around the map in order to stay hidden.
If you have a friend playing with you try to get him defending and alerting you of incoming enemies from the sides. You can also ask random people nicely. The combat Engineer pairs well with the Sniper, providing fair defense, health and ammunititon.

How to counter: Okay, just listing these: Scout,Sniper,Spy. Sniper vs. Sniper is the thing you should be used to. Protect your own team by getting the First Blood buff from him! Scan for the usual sniping spots where you're most likely to spot him.
Scout will work extremely well, as long you don't huddle in his sight for too long.
And Spy works well, because- Do I really need to explain? Fine. Invisibility --> behind the Sniper --> Backstab/Revolver. Simplicity itself. Well at least when talking about Snipers... Move on to the Spy segment.

How to play: This is a bit of a step to the unknown with me, because I don't play Spy. Anyway, Spy is really hard to play in Arena, where there are small amounts of players and everyone's watching their backs.
You'll notice you're using your primary weapon alot more than in other game modes. So get familiar with your revolvers. Remember, every bit of damage counts! Amby and stock work the best here. Avoid crowded places, and stab any campers or pre-occupied enemies in the back. And we have come to this... Me, a loyal hater of the Dead Ringer. Yes, it is the best watch to use here. The damage reduction is insane and should make for a near perfect escape.
Spy-cicle also helps to extinguish afterburn so you don't lose any excess health. Use alternative routes and chip away the enemies' health.

How to counter: Pyro still works fine, but chasing Spies is much harder when it's normally just you and the Spy. Ignite the Spy, and hope he doesn't feign death or use the Spy-cicle. He's normally gone like a fart in the Sahara desert after that. But what does work the best?
Scout. Since Spies use their revolvers much more, dodging becomes a bigger part of gameplay. Approach them, and activate their Dead Ringer. Make sure to steal the healthpacks, if possible. That's when capping comes in.

I feel like TF2 wiki does an amazing job giving you helpful tips in each of the official Arena maps, but I feel that they are still somewhat minor things, so I will just be redirecting you there.

Badlands

Granary

Lumberyard

Nucleus

Offblast

Ravine

Sawmill

Watchtower

Well

So here it is. My first ever Steam Guide, which was really fun to make, as I like preaching about doing the right stuff to everyone. Which drives my friends nuts :3

So if you liked this guide/thought it was useful, please take the time comment if you see anything out of date, misspelled, or think I should add something or remove something. Who knows, I might have forgotten a whole chapter! I will also try to keep updating this if new things come up to my mind.

Also, I realize lot of people like to read guides thoroughly, but forget to rate it, so please rate this guide up if you thought it was useful, or vote it down if you think this a piece of garbage.