When your party walks into a dungeon, you get your own copy of it. Nothing has been killed before you arrive and no other group is on the stairs.
Who to talk to
The captain of the guard keeps the way in, a short walk up from the quay where every new character arrives. Right click him and ask about dungeons, and he shows you every one he can send you to, what each pays and whether you are ready for it.

He will not send you somewhere you cannot go. If your level is too low or your party is the wrong size, he tells you before you set off.
Picking one
Some dungeons are short and forgiving, good for learning on and fine to run on your own. Others go down several floors and want a full party, with somebody to take the blows and somebody to keep everyone standing. Start with the easiest one he offers.

Going in
Whoever is leading takes the party in and everybody goes together. Clear the floor and the way on opens. If the stairs will not let you through, something is still alive. Look in the corners.
Getting out
There is a Leave button at the top of the screen for as long as you are down there. Press it and you come back out where you went in.
If your connection drops, you have a short while to get back in before the run ends. Leaving costs nothing, and you can try again another day.
What you get for it
Experience and gold every time you finish, and something extra the first time. The party is paid after everybody is back on the surface.
Before you go
- How a fight works, particularly the part about backing off.
- Dungeons, for how a run goes from top to bottom.