Congratulations! You have officially became a Terrarian, and are playing Terraria! In this guide, I assume you know a decent bit about the game already. By this, I mean I won't be going into boss strategies or recommended equipment for boss fights. Let's get straight to the point- after creating a new world/character, you should start collecting basic resources like wood, and stone, with the copper tools you start out with,Once you have a decent bit, you should start killing some slimes to collect gel. I recommend making lots of torches with wood and gel. Now, it's time to build a house. I'm not going into details on house requirements, but I will go over the basics. Begin constructing your house by making a rectangle out of wood (preferably 5 tiles high, and about 10 tiles wide) now, take out the bottom three pieces of wood on one or both sides of your house. With your wood, craft a work bench. place this down, and craft one or two doors (depending on how many entrances you have), a chair or comfort item, a table (the work bench works as a table), and a fair bit of wood walls. Place the walls in the backround along with the rest of your things (chair, table, etc.). Now, all you have to do is place down a torch or light source, and your ready to go! Your guide can move into this house. Build more houses for more NPCs to move in (along with their individual requirements). At your work bench, craft a Wooden Sword, a Bow and plenty of arrows, a furnace, wooden armor, and maybe a wooden hammer if you messed up on the house walls, or want to change the shape of a few blocks in your house. This is what I call the "Wood Stage," which is right at the start.

With the basic wood gear, it is time to go under. By now, you should have gone exploring the surface of your world for chests, and pots. Loot and break all of these, as they could contain good items. When you explore the surface, you should find a cave. Use torches, glowsticks, or shine potions to light up the cave, as you go down. Mine any ore you come across, and be cautious as there could be far drops. Underground, you should find Underground Houses with gold chests, generic chests, life crystals, and ore. Be careful underground, as there could be traps, so always keep an eye out for pressure plates. Once you collected enough ore, go on up and preferably place down a chest to store some items. TIP: It is always smart to keep your chests organized. Whether you world has lead or iron, smelt it into bars at the furnace and make an anvil out of 5 bars. You can craft gear/tools/weapons at an anvil.
Here is a nifty little ore guide of what your world got blessed with:
Copper = Tin
Iron = Lead
Silver = Tungsten
Gold = Platinum
PRO TIP: Although Silver is equal to Tungsten, a Tungsten pickaxe can mine meteorite, while a silver one cannot.
You should gather a LOT of bars- enough to make full iron/lead armor or better, and some better tools (try to get a Tungsten/Gold/Platinum pickaxe for the next stage).

This is the stage that I completely recommend- the Meteorite section. Basically, you need to summon and harvest a meteorite. To summon a meteorite you have to break at least one shadow orb or pulsating heart. In the 1.3 update, they added a loading screen which shows a green side, and an either purple or red side. Purple = Corruption, and Red = Crimson. Follow the following guides accordingly:

Crimson
If you have a crimson world, find it on your surface- it should be a reddish biome. Once you do, fend off the monsters and EXTREMELY CAREFULLY venture down into a tunnel in a reddish-block-hill. I recommend building a wooden cage around yourself, and slowly extended it as you go down. Once inside, there should be beating hearts. Break at least one of these with explosives. (If it is in a cage of crimtane blocks (reddish blocks), blow that up with either bombs or dynamite. Find these explosives in chests or from a demolitist. TIP: Bombs and Dynamite will blow up your cage partially, and hurt you if you are to close to the explosion. When you blow one up, you should get a The Undertaker. After destroying one, go back home, and wait for a meteorite to land.

Corruption
If you have a corruption world, find it on your surface- it should be a purple biome. Once you do, fend off the monsters and EXTREMELY CAREFULLY venture down into a deep, hole. I recommend building a wooden cage around yourself, and slowly extended it as you go down. Once inside, there should be purple bulbs. Break at least one of these with explosives. (If it is in a cage of ebonstone blocks (purple blocks), blow that up with either bombs or dynamite. Find these explosives in chests or from a demolitist. TIP: Bombs and Dynamite will blow up your cage partially, and hurt you if you are to close to the explosion. When you blow one up, go back home, and wait for a meteorite to land.

WARNING: DO NOT BREAK 3 SHADOW ORBS/PULSATING HEARTS

Dealing with the meteorite
When a meteorite lands, it should come up in the chat. Venture out to find it on your world, and harvest it CAREFULLY. Stepping on meteorite WILL burn you/set you on fire. Also fend off the meteorite heads. TIP: Meteorite heads have low health, but strong attack, and can go through blocks, so I recommend building platforms to step on while harvesting it with either a Tungsten, Gold, or Platinum pickaxe, or with explosives. Smelt this into bars at a furnace and make full Meteorite armor and a Space Gun. The meteorite full armor set bonus is the space gun uses no mana. I find that this setup can basically carry you through the rest of Pre-Hardmode. I've even defeated the Wall of Flesh with it personally.

Just a healthy reminder that gaining yo-yos as you go would be very good, as they can be quite useful in the game. Wooden Yo-yo: Wood and cobwebs. Also, try to craft boss summoning items as we go. You can look those up on the internet. ;)

By now, you should have aquired some boss-summoning items, like the Suspicious looking eye, which is crafted at a demon/crimson alter or found in gold chests. Use this to summon the Eye of Cthulhu at 7:30 (beginning of night time) in-game. I won't go into detail on strategies, but upon defeating him, you should receive crimtane or demonite ore. Smelt this and make some stuff out of it. Now, defeat the world-special boss in your world. Break 3 shadow orbs (Eater of Worlds) or pulsating heats (Brain of Cthulhu) to summon them. THis boss should drop more crimtane/demonite AND shadow scales/tissue samples. Use both of these to make even better gear- Crimtane/Demonite armor and Deathbringer or Nightmare pickaxe. Kill the queen bee in the underground jungle, in hives, by breaking a larva or using an Abeemination. Kill skeletron at the dungeon at night by using the old man that spawns there, by hitting "Curse"
WARNING: DO NOT GO INTO DUNGEON PRE-SKELETRON - You will die instantly from a dungen guardian, although after skeletron you can roam freely throughout the dungeon. Although dangerous, the dungeon can behold some pretty good loot. Other than that, you can go just into the top bit. If you find a blue book with one grey stripe, break it. It is water bolt- which is a very powerful early game weapon. You can use the water bolt to shoot into the sky. If it bounces back, build up. There is a floating island, which can have some good loot, like a lucky horseshoe, which makes you take no fall damage. This is useful for hellevators. The last pre-hardmode boss, is King Slime. summon him with gel and a platinum/gold crown, or kill at least 150 slimes during slime rain. These will all lead up to the final pre-hardmode/early hardmode boss, the Wall of Flesh.

Ah... the Wall of Flesh. The gateway to hardmode in your world. The wall of flesh is a boss that borders the permanent change to hardmode. It is pretty tough. First things first, you need to build a hellevator. This is a vertical hole that runs all the way from the surface to the underworld. I recommend using water buckets to turn lava into obsidian. Mine this with a Deathbringer or Nightmare pickaxe, to craft an obsidian skull, that gets rid of setting you on fire from stepping on meteorite and hellstone. Also grab a hellforge which looks like a furnace but red. Mine lots of hellstone and obsidian. Be warned though- upon mining hellstone, it turns into lava. I recommend mining it with a one block thick wall in between you and the hellstone. Craft obsidian and hellstone ore into hellstone bars at a hellforge. Try to make full molten armor and some molten gear. You HAVE to make a molten pickaxe to proceed though, and I recommend a Fiery Greatsword as well as a hellstone bow. Now, it is time to make a bridge. Build a VERY long (1000+ tiles recommended) bridge across the underworld. While in the underworld, try to find and kill a Voodoo demon. They drop a Guide Voodoo Doll, which is used to summon the Wall of Flesh.
!IMPORTANT!
NEVER kill a voodoo demon over lava- it will summon the WoF. Also, you must have a guide alive in your world to summon the WoF.
Summoning and Fight
You summon the WoF by going to the edge of your bridge, and throwing the Voodoo demon in lava. This will summon it, as well as kill the guide. It will grant a debuff that kills you if you try to go home. The mouth burps out leeches ocasionally, the eyes shoot lasers, and The Hungry stick out of it. I recommend killing off the Hungry with a sword first, then shooting the eyes with a gun or bow. (You can shoot the mouth, but the eyes have 0 defense, while the mouth has 12). Once defeated, the WoF will leave a square which includes the Pwnhammer, and some other valuble stuff. You are now in hardmode.

Hardmode is a lot harder then Pre-Hardmode, but has better loot. With your Pwnhammer, smash three crimson/demon alters. These will bless your world 3/6 hardmode ores. They can be:
Palladium = Cobalt
Orichalcum = Mythril
Titanium = Adamantite
With the molten pickaxe, you can mine Palladium/Cobalt. With this, craft it into bars, and make a palladium/cobalt pickaxe. With this, you can mine Orichalcum/Mythril. With Orichalcum/Mythril, i recommend making armor and an orichalcum/mythril anvil, which is used to craft O/M gear/armor. With an O/M pickaxe, you can mine Titanium/Adamantite. You have to smelt these at a T/A forge, which is made from a hellforge, and 30 or the corresponding ore. These are the basics of the hardmode ores. To mine these, you should probably use your hellevator to find caves with them and spelunker potions.
IMPORTANT:
When you enter hardmode, the Corruption/Crimson and Hallow start spreading. You need to find a way to stop this.
You should also aquire wings at this stage. I personally recommend Harpy Wings. They give you a good flight range, and are easy to aquire. You just need to go up to a floating island preferably, farm harpies until you get a Giant Harpy Feather, and harvest Wyverns to aquire 20 souls of flight. Then craft them at an O/M anvil.

The mechanical bosses are the easiest Hardmode bosses. I recommend to fight them in this order:
-The Destroyer
-The Twins
-Skeletron Prime
I wont go into detail on killing them, but will give you a little advise:
-The Destroyer:
Build a small arena out of platforms, and use a megashark (or minishark) with crystal bullets, a nimbus rod, and a star veil, and shoot down at it, while destroying the probes.
-The Twins
Build a long skybridge with campfires/heart lanterns. Use a megashark with crystal bullets, and hermes boots, spectre boots, lightning boots, or frostspark boots (boots that speed you up).
Shoot the twins while running backwards across the skybridge. You may need to turn around occasionally.
-Skeletron Prime
You can use the skybridge from the Twins battle, and just shoot at it while dodginge its attacks with wings, fly around it, using wings and a megashark with crystal bullets.
With the Hallowed bars and one of each of their souls, build the Drax, or Pickaxe Axe. Next, go the the jungle, to mine chlorophyte. I recommend using a splenker potion for this. Make armor and tools with this at a T/A forge and an O/M anvil. You can use chlorophyte to make armor and tools and shroomite to make a hoverboard.

Beating plantera with this gear makes Plantera very easy. Basically go into the underground jungle, and look for Plantera's bulb. Carve out a big arena around it. Use platforms and campfires/heart lanterns. Use a megashark with crystal bullets. Circle around plantera while shooting it, and you should win fairly easily.
Next, is golem. Golem is found in lihzahrd temples. One spawns in your world in the underground jungle, but often spawns incorrectly or not at all. Be careful, as lihzahrd temples are crawling with traps, so I recommend a mechanical tool like a wrench or wire cutters. If a temple spawns, you can collect lihzahrd power cells from lihzahrd chests within the temple. Use these to summon golem at a lihzahrd altar. I recommend killing the golem's fists first. Now, take down the head. When that reaches half health, it will start shooting lasers at you. These can go through blocks, so you have to be careful. The less health the head gets, the more frequent the lasers get. When the head dies, it flies around, and the body gets vunerable. The head still shoots lasers, so be careful. Once you kill the body, it drops its regular loot.

Duke fishron is a fish-like boss that flies around very quickly. I recommend using asphalt and boots that increase your speed, and wings. I highly recommend building two of these asphalt bridges- one higher up, and using a gravitation potion, as the fight is drastically easier. Fly around very quickly, dodging his attacks. I recommend using at least a megashark, and chlorophyte bullets. Pop the bubbles he shoots at you, and dodge the sharknados. The fight isn't exactly intended to be post-golem, but I recommend it.

To begin the Lunar event, you have to begin by killing golem. Now, there should be 3-5 devoted cultists at the dungeon. Upon killing all of the cultists, the Lunitic Cultit will appear. He will use many spells to attack you, and occasionally spawn spectral dragons, which are similar to wyverns. Know that they don't drop anything- even hearts. I recommend spectre armor, and razorblade typhoon to kill the cultist.
Once he dies, the four celestial pillars will spawn at pre-determined locations around your world. They are: Nebula Pillar, Vortex Pillar, Solar Pillar, and Stardust Piller. They represent the four classes of Terraria, such as; Solar for melee, Stardust for summoner, Nebula for ranged, and Vortex for magic. You have to kill 100 of the unique monsters that spawn at each pillar, in order to destroy the shield around the pillar. Then, the pillar becomes vunerable to attacks. Each pillar drops fragments of its kind, which are used to make end game items that can be useful against Moon Lord. I recommend backing up your world and players after the third pillar so that if you fail the Moon Lord fight, you can always reload your things, and not have to start over from the Lunitic Cultist.
The Moon Lord is intended to be the final boss of Terraria, and is EXTREMELY HARD. Proceed with caution. After defeating the fourth celestial pillar (or using a celestial sigil made of 20 of each lunar fragment), a message comes up saying, "Impending doom approaches," which indicates that the Moon Lord is on his way. About a minute later, Moon Lord spawns. I recommend the Solar Eruption to kill him with or the Phantasm, which both work great, and are crafted from pillar fragments, at an ancient manipulator which is a 100% drop from the lunitic cultist. Try to get a rod of discord to dodge his laser, while you attack his hands and his forehead. Also, the cosmic car key helps out alot. Try to dodge his attacks as well as the True Eye of Cthulhus. Once his hands and forehead are defeated, his heart becomes vunerable to attacks. Destroy his heart, and voila! You have defeated the Moon Lord, and obtained some of the BEST items in the game, like the Meowmere and the Last Prism, just to name a couple.
Another strategy that I personally favor is to build a room in the sky with the nurse in it, so that when you run low on health, you can heal up. The room will block the lasers, making you take less damage. This is the cheesy way, but is effective. For maximum efficiency in singleplayer, put your world on auto pause so when you click the nurse, the battle pauses, and you can heal, calm down (the fight is very intense), etc. Note that this is cheesy, so if you want to beat Moon Lord completely legitimate, this isn't the strategy for you.

Invasions happen randomly, or from specific items the five current invations include:
-Goblin Army
-Pirate Invasion
-Frost Legion
-Solar Eclipse
-Martian Madness
In that order, from easiest to hardest, and the point in the game you are likely to encounter them.
They can get you some epic loot, like the cutlass from the pirate invation, and the cosmic car key from the martian madness invasion. In order to summon them goes as follows:
Goblin Army
To summon a goblin army, you can just have it spawn randomly, use a tattered cloth, (which is dropped by the goblin scout) to craft a Goblin Battle Standard, or let a goblin scout live after encountering one.
Pirate Invasion
To summon the pirate invasion, you need to let it spawn randomly, or use a pirate map that drops from enemies in the ocean biome at a 1% chance during hardmode.
Frost Legion
To summon the frost legion, you need to use the snow globe, which is found in presents in a 1/14 chance in hardmode.
Solar Eclipse
To summon a solar eclipse, you need to wait for it to spawn randomly after the WoF and at least one mechanical boss has been defeated, or use a solar tablet which are found in Lihzahrd chests, or crafted from 8 solar tablet fragments which drop from Lihzahrds and Flying snakes.
Martian Madness
To summon the martian madness event, you need to encounter and not kill (or trigger its "beam") a probe which randomly spawns in you world after the defeat of Golem.
Other events are geared towards endgame players, so summon with caution, but include:
-Pumpkin Moon
-Frost Moon
How to summon:
Pumpkin Moon
To summon the pumpkin moon, use a Pumpkin Moon Medallion, which is crafted from 5 Ectoplasm, 10 Hallowed Bars, and 30 Pumpkins at a mythril or orichalcum anvil. The moon can be only summoned at night, lasting until morning, and progressing through 15 waves, and 5 bonus waves. Note also that the event can only be summoned in hardmode.
Frost Moon
To summon the frost moon, use a Naughty Present, which is crafted from 5 Ectoplasm, 5 Souls of fright, and 20 silk at a mythril or orichalcum anvil. The moon can be only summoned at night, lasting until morning, and progressing through 15 waves, and 5 bonus waves. Note also that the event can only be summoned in hardmode

In conclusion, this has been my guide to terraria on prograssing through the game. There are still ALOT of things i didn't cover, but these are the basics. I hope you learned something, and overall, thank you for reading this, because it took a LONG time to write. Please leave any troubles or problems in the comments along with any grammatical errors you come across. I hope to answer any of the questions you leave in the comments, and thats about it- Goodbye!

P.S.- This guide was initially written soon after the release of 1.3, and doesn't include anything added in 1.3.1, ,1.3.2, 1.3.3, 1.3.4, etc., as I do not play the game anymore very much. If I feel like it, I might familiarize myself with the updates and update the guide.