The Mine is located on the north east of the map and easily accessible. The Mines are opened on the fifth day of the game. You will find a letter in the mail by Joja Corperation, saying that the mine has been cleared. When you go to the mine, you will find an NPC who claims to be an adventurer. He gives you a sword and invites you to go down into the mines at their own risk.
To go down a level in the mines, you need to find the ladder down. It is either under a rock, unlocked after killing an enemy, or out in the open. there can be multiple ladders down.
The maps are usually the same, and the exits can often be found at the same place every time, usually under light sources (torches).
You can exit the mine at any time by going up to the ladder and selecting the "Leave the mines" option.
After every five levels, you unlock a checkpoint that can be accessed by the elevator. You will be able to start from that point each time you come back.
After every ten levels, there is a chest with a unique and powerful item inside.