I'm writing this from the perspective of having entered from the Wolf Pit.
Once you've come up the ramp you'll immediately be attacked by two bandits. Once you've dealt with them, stay in, or enter combat mode and head towards the right. There's a thug mage in this group of bandits who will cast sleep on you, and you want to get him out of the way as soon as possible. Once you've killed this group of bandits make sure to check and see if any of them have dropped decent weapons, and there's also some First Aid Kits on a bench against the wall if you want them.
**NOTE: This is one of the best places to equip yourself with halfway decent items early in the game. By the time you leave your entire party should have at least Iron Short Swords and Leather Armor. Note I mean Leather, not Poor Leather. Don't forget to check the bows if you have an archer in your party, as there are sometimes a couple Ash Bows lying around, as well as some Iron Javelins if you want someone to use thrown missiles.**
Once you're done in this first room open the doors to the south. There's a group of bandits, and one apprentice mage in here, so it's best to enter already in combat mode. The apprentice mage sometimes drops a healing potion.
Now check the rooms to either side, and you'll find an archer in each one. Check the dressers and chest in the room to the west for some coins, and one of the crates in the room to the east has some dried meat. The small room off this room contains a chest, which used to contain their loot, but it's not there anymore.
Go back to the middle room and then go south again. This is kind of the same set up, except that it's all one room and there are two archers on each side. The benches in the middle contain mostly stone arrows, but there are also a few iron ones and some iron javelins.
Now go back to the area where you battled the Thug Mage, and go either south or east, doesn't really matter which way you choose first, but be aware that there are a few bandits wandering around on either side, and you'll probably bump into them. Follow the passage along the side of the rooms you were just in until you get to a section where it dead ends with a pink section of wall. These pink sections are actually secret doorways, and you can go through them. You'll find some items on either side, but nothing to really write home about. There's also some more bandits out here, but I've found them to be rather unpredictable in when and where they appear.
Now head along the front of the lair to the east and follow a long passage to the trash pit. There's a couple cave slimes back here, and a lamp and a set of lockpicks. You can go over to the west side now if you want, but I usually wait, for reasons you will soon see.
Go back into the Bandit Lair through one of the secret doors, to where you first entered from the Wolf Pit. Just to the side is a passage leading up. Go up the passage and through the door to battle a few more bandits. There are two locked doors at the top of this room. The one closest to the water reservoir contains a few good items, including a strength potion, a curing potion, some healing herbs and a few other minor goodies. The other room contains a little bit of food. If you turn the wheel in the corner it will open the portcullis, which leads to the passage that goes back to the front of the Lair on the western side, and there's also a few rats.
Go back through the portcullis and follow the short hall down until you reach a door leading to the west. Go through it and pick up a healing potion, and some energetic herbs from the dresser. Go through the next door and you'll find yourself in the Bandit Temple. There's an evil priest and some bandits to kill, and I sometimes find a Steel Short Sword after I've killed everyone.
Leave the temple the way you came in, to avoid having to pick the lock, and go back into the short hallway. If you go through the doorway at the end of the hall you'll find yourself in a small room with the locked door to the temple, and a door leading to another passageway.
Go out into the passage way and down until you reach a branch leading off to the west. Go through here and enter the pen to kill a few wolves.
Next, go up towards the north. There's a couple cows there, just leave them alone. Enter the only doorway and you'll find yourself battling the Bandit leader who has a thug and an apprentice mage for company. The Bandit leader sometimes drops a Steel Spear. Once you've killed them enter the small room at the bottom to pick up a Wand of Bolts and a few other minor goodies. Don't forget to check the chest for coins. Now go up to the top of the room where you battled the Bandit leader and enter the bedroom. There's a few coins in the chest.
Now stand beside the dresser to the north, and push against the wall. You'll find yourself in a chamber with lots of swampy patches, and a chest. There's a few traps on your way to the chest, which will poison you if you don't manage to disarm them. Open the chest, disarming another trap, and get the coins.
Now all the way back down to the front of the Bandit Lair and out into Upper Avernum. There's some bandits guarding the tunnel, and they'll attack you when you sneak up behind them. Once you've dealt with them it's back to Fort Emergence to get your reward from Commander Johnson. You should have gone up a few levels by now, so don't forget to go to the training hall to use your skill points.