Upon arriving at the dungeon (Either to the far west/east) for the first time, you will see an old man with a bow in his left hand. Entering without restricted access causes at least 1 dungeon guardian to spawn and kill you in a single hit. If you have 300-500 max life and at least 10 defense and if it's night, you can talk to the old man and select the Curse button, causing him to turn into Skeletron.
After you kill skeletron, you will gain restricted access, and dungeon guardians will stop spawning.

Always:
Dungeon Slime*** - An enemy which carries a golden key that is for unlocking the gold chest. Has 150 Normal Health and 300 Expert Mode Health.
Angry Bones - Has four variants.
Dark Caster - They are weak and senseless. They have 50/100 health, and a couple defense. They have low damage.
Cursed Skull - A flying skull that can curse you.
Spike Ball - They don't take damage like the Blazing Wheel and True Eye of Cthulhu.
Blazing Wheel - A trap that moves very quick. A light source.
Dungeon Guardian* - Cannot be killed. They can kill you in one hit.
Skeletron** - The first boss that appears in the dungeon.
After Plantera Dies:
Armored Bones - Each version has four variants.
Paladin - A heavy armored mini-boss.
Necromancer - A hard mage to kill.
Ragged Caster - Stronger than the Dark Caster.
Diabolist - A rare Ragged Caster.
Skeleton Sniper/Commando - They are gunners that wield weapons.
Tactical Skeleton - Undead SWAT gunners
Giant Cursed Skull - The upgraded version of the Cursed Skull.
Bone Lee - An undead ninja and thief.
Dungeon Spirit - A rare enemy and the only one that drops Ectoplasm.
Post-Golem:
After Golem is defeated, you will encounter four cultists.
Lunatic Devote - The ritualists which don't deal damage.
Cultist Archer - They defend the lunatic devotes.
Lunatic Cultist**^ - The leader of the dungeon coven and the second boss that appears in the dungeon.
* Appears before skeletron is defeated.
** Boss.
*** Rare Creature.
^ Killing the lunatic cultist initiates the Lunar Events, showing the status message "Celestial Creatures are invading!"

In the dungeon, you can find books, water candles, dungeon crates from fishing, alchemy/bewitching tables.
You can find the Muramasa, which is like the phasesaber. It is a drop from an enemy. There is also the rainbow gun, which is required for the Rainbows and Unicorns achievement. A yoyo named Valor can be found in golden chests too.
There are also spikes. You can trash the water candles if you break them. You should always avoid spikes. There is a background object that can't be plundered called the mysterious tablet when Golem is defeated.

1. Never enter without restricted access. (Causes a Dungeon Guardian to kill you in one hit)
2. Do not touch spikes. (Spikes are traps)
3. Don't approach Blazing Wheels and Spike Balls. (They cannot be destroyed)

Randomly, you can encounter the mechanic when you have restricted access. She will first appear tied. Rescuing her will make you acquire her.

BRICKS
SLABS
TILES
OTHER

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Robbing the Grave: Obtain a rare treasure from a difficult monster in the dungeon
http://hydra-media.cursecdn.com/terraria.gamepedia.com/e/ee/Achievement_Boned.png?version=9397f59661789ec376959d9ef925c0bd
Boned: Defeat Skeletron, the cursed guardian of the dungeon
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Dungeon Heist: Steal a key from the dungeon's undead denizens, and unlock one of their precious golden chests
http://hydra-media.cursecdn.com/terraria.gamepedia.com/d/d2/Achievement_Big_Booty.png?version=5e6beb6dac5fb83dbaec36c4559b4d97
Big Booty: Unlock one of the dungeons large, mysterious chests with a special key
http://hydra-media.cursecdn.com/terraria.gamepedia.com/6/64/Achievement_Obsessive_Devotion.png?version=86ccdb5cf8d4dd9a4619b0b22bf83c71
Obsessive Devotion: Defeat the Ancient Cultist, fanatical leader of the dungeon coven
http://hydra-media.cursecdn.com/terraria.gamepedia.com/1/19/Achievement_Rainbows_and_Unicorns.png?version=fcd5e3ee9d4cda25c387c2ab1b4977ca
Rainbows and Unicorns: Fire a rainbow gun while riding on a unicorn*

*Requirement for the Rainbows and Unicorns achievement

The dungeon is always on the other side of the jungle. If you locate the jungle, go the other direction. (One side has the jungle, and the other has the dungeon)
The snow biome spawns close to it. (It's also on the other side of the jungle)
In HERO's 9th episode he was killed by a dungeon guardian while in werewolf form. In the 12th, he encountered four queen bees without the moon charm equipped.

This shows all the wiki images for the dungeon.

http://hydra-media.cursecdn.com/terraria.gamepedia.com/thumb/b/b1/Dungeon_Map.png/200px-Dungeon_Map.png?version=5933831db4aa44fbd3e05f6772d6ead6
How the dungeon can be generated

http://hydra-media.cursecdn.com/terraria.gamepedia.com/f/f3/Dungeon_Wall_Types.png?version=1da7888c275711df30f57e08d9004d44
Brick, Slab and Tile types

http://hydra-media.cursecdn.com/terraria.gamepedia.com/5/5a/Water_Candle_%28debuff%29.png?version=d13038c78fe0abea754a1866978ec53f
The water candle debuff can happen in the dungeon

http://hydra-media.cursecdn.com/terraria.gamepedia.com/f/f4/Mysterious_Tablet.png?version=5b715134f54a53ac337a70d0294c84fc
The Mysterious Tablet

http://i.ytimg.com/vi/D0avno4bUgo/maxresdefault.jpg
The Lunatic Cultist

If you have found the jungle or the snow biome, label a comment. They should all be nice. You should also label a comment if you encounter the Old Man, Dungeon Enemies or Cultists.