I'm gonna be covering the competitive aspects of fistfights. If you want to just run arond and have fun, you're free to do it, I don't judge. I mean I won't show you many pro tricks, just how to do better in competitive. Also english is not my native language, but I'm trying.

Motivation is important.
You gotta be motivated, cuz people will kill you no matter how good you are. There always will be that cheeky basturd with smith, sniping you across the map, or dude with two revolvers not letting you get close enough, or gang bang gang of 3-4 people. You just have to accept it.

First of all
Get some sweet mods. You can get any, but there are two you totaly need.
1-Dio Brando Ranger Mod
2-Fancy gloves mod. (Or this one)

Then
1-Get in a server
2-Go Rangers, there is no other way.
3-Get this loadout (I'll explain everything)

And there you are. Time to start the punching.

So you may ask me "Oh glorious master, what the kek do I need all this things for?" I'll answer, but don't use kek anymore, it's an old meme.
Brass-Knuckles - you need the damage man.
Boots - Kicking is as importnant as punching, you should take them with any loadout really.
Deringer - You'll see later
Quick draw and Right-handed - For using Derringer
Dio Brando mod - Jojo's is the best thing ever happened to humanity.
Got it? Good.

So there are the things you need to know about FoF fistfighting.
1- LMB - Punch with left hand, the faster attack, prolly deals less damage than RMB, strikes faster totaly.
2-RMB - Punch with right hand, slower but stronger attack, prolly deals more damage than LMB, strikes slower.
3-Headshots do more damage (about 30) (Regular are about 9-18)
4- You can knock the gun out of someones hands. It's not guaranteed. You have to be face to face with your opponent, otherwise it simply doesn't work. RMB to the face knocks the gun out of the hands 90% of the time.

Now the Combos
1-Face to face
Punch + Kick + Derringer
1 Derringer shot is not enough most of the time, so shoot your load the second time.
Remember to RMB in the face.
2-Flying kick
jump forward + kick
You can kick mid-air, It's awesome. You can kick even while you're falling.
3-Barrel Abuse
Find a barel + press E + throw barrel at enemy + pick it up again + throw it again
If you hit the enemy twice he's dead. Barrel throwing deals about 65 dmg. Be careful, barrel might blow up even if you don't shoot it.
4-Super defence
Find a crate + prees E + hold it while you run up to your target
You brake the crate with one punch or one kick. How fast will enemy break your crate depends on what weapon is he using. Most efective against dumb smith players.

Tips
-Try to kick people into the walls and the corners, rather than into open space. Exept when they fall to death.
-Disarming people is rly useful.
-You vs 3-4 people from the same team is a fight already lost.
-You vs 3-4 people from different teams is still pretty poor chances.
-Don't just run straight into your oponent. Try to strafe.
-You might as well change Derringer to any other pistol. Infact, you should.
-Y not start with a better gun? Because Derringer is only two points, you need the quick draw so u can pull off the Face to Face combo.
-If enemy can't see you and opened up his back, run after him and punch him in the head until he turns around, then use Face to Face.
-You get alot of points (13 for fist kills, 10 for kick kills, 8 for derringer kills, 15 for barrel and fall to death kills)

Any ranged weapon
Run up to your target, if you're not dead, RMB him in his face, he lost his gun, punchkick him to death.
Any melee weapon
Pull out your derringer, press Alt and shoot it untill it stops eather running at you or moving.

If you're unhappy with this build including so much stuff beside just fists, you can try including less. I'll tell ya what happends when you exclude stuff.

Derringer ftw, it's not even related to fists - face to face engagements get alot harder. But you can manage it. I belive in you.
Kicks? I thought this guide is called How to FISTfight - This really just makes your life harer, but still, if you disarm people you still manage to pull off kills.
Derringer? kicks? I ain't using any of this gay ♥♥♥♥♥♥♥♥♥ - Man you just want to make you're life harder aren't you? You know you're not playing against bots right? You can't circle strafe them. But okay, again, disarming people might get you some kills.
I am a hardcore fistfighter! I won't use anything, even brass-knuckles! - You might as well just disarm your enemy to take his revolver and shoot yourself. It's not viable in any way.

This guide is 100% based on my experience playing this game. If you want more precise numbers search for the wiki or something. And yes, I realise this is basically just a fist-related build guide, but meh whateva. Share your fistfighting tricks in the comments. Thanks for reading. Sorry for my English. Bye.