The best way to enter this area is by water. You'll find yourself at the docks, in an area guarded by two Rogue Warriors.
Go through the doors and into the base. You'll find yourself in a long hallway, with lots of doors. Head to the north first. The first door to the east leads to the cult's training room but is pretty much empty.
The next door to the east leads to the "Purification Chamber". There's a Rogue Warrior in here, and a bunch of small cells.
The northern door at the end of the long hallway leads to a storage room with a lot of miscellaneous items. Check and see if there's anything you want to take with you.
The three doors leading to the west are the northern guardroom. There's a couple Rogue Archers and a Rogue Mage in here. One of the archers sometimes drops a Fletchers Ring, and there's a wand on the table.
Back into the main hallway and head down past the two doors across from the docks, ignoring them for now. The doorway just to the south of the docks leads to what appears to be the living area. There are a few cult members in here.
Keep going south and then west. You'll find yourself in the second guard area, this one containing some Rogue Archers and an Evil Priest. Once you've disposed of them, go through the door just to the east of where they were and enter the small storeroom. One of the barrels contains a Strength Charm.
Head into the short hallway that leads east from the main room. There are only two doors leading off of it. The first door is a room containing a Bladesman. Once you've killed him, check the chests. One of them contains a Marble Key.
The next room contains the Cult Leader. Once you've killed him walk along the bookshelves to pick up another Marble Key. You only need one, but since you can have both...
Now go to the double doors across from the docks. Through this doorway is a courtyard with some more cult members. Once you've killed them you might want to go through the doors to the south. Use either Dispel Barrier or a Piercing Crystal to get through the barrier, then head to the end of the passage. Go along the outer wall to the east. There's some Iron Plate Mail and coins lying on the ground. If you don't have the spell or a piercing crystal there's a back way out of the building and you can walk around to this area from there. See the map for the doors, marked 15 on the map. The two western ones lead to outside the complex.
Once you've cleared this area go through the southern of the two western doors in the courtyard. This will lead you into a long winding passage, with three pools of water scattered along. Touch each of the pools to bypass the traps in this area. There's also some Spiritual Herbs on a bench near the third pool.
At the end of the passage is a door leading to the storage area for special items. The first chest to the west is empty, and the one across from it contains a spellshard. The next chest to the west contains the Orb of Thralni, and the one across from it contains a Bar of Uranium. This bar will periodically poison your entire party if you take it, so it's best just to leave it alone. The next chest to the west is empty, and the one across from it contains a suit of Cursed Plate Mail. Now head back through the passage to the courtyard.
The last door leads to a storage area guarded by a Rogue Archer. There's quite a few items in here, but the most important one is a pair of Iridium Pants. Now go down to the northwest corner of the room and check the wall for a secret passage. There's a few more items back here, including a pair of Nimble Gloves.
For a little bit of humor go through the door in the northeast corner of the storage room to read the memorial plagues on each pedestal.
Now head through the doors near the secret passage. There's a small storage room off of this room with some very mundane items.
Now walk into the portal. You won't get through this time, since you'll be attacked by a medium sized group of cult members. Once you've killed them go up the stairs and push the button on the control panel. Now walk into the portal again and you'll find yourself teleported to a spot near the back of the Bandit's Lair in Upper Avernum. Return to Fort Emergence to tell Anaximander you've completed the quest. He'll let you keep the Orb of Thralni, which will come in very useful throughout the game, and is necessary to finish the Golem Quest.