Upon first entering the Troglodyte Altar you'll receive a message about the quietness. For now, check out the northern wall right near the entrance for a secret passage. You'll have to cross some lava and disarm a trap to reach a storage room containing quite a few Elixirs and some armor. You may want to equip the armor, and you definitely want to pick up the elixirs.
Now head back into the entrance room. There are two sets of stairs leading up, and two passages leading off the room, one to the north and one to the south. The northern passage leads to a water reservoir and a storage room, but the storage room doesn't contain much of any worth.
The passage to the south will take you to another water reservoir, but this one has some Healing Herbs on the ground. Check out the storage room on this side for some Gremlin Wine.
Now head east, choosing either the stairs or one of the side passages. Whichever way you choose, when you approach the eastern edge of the map you'll have to fight a battle with a variety of Troglodytes. Clear the map by crossing the eastern portion of the map, either north to south, or vice versa. The middle section contains two living statues as well as the Troglodytes, so you'll have to kill them too.
Just north of the living statues, in a little alcove is a Slith statue holding a Fine Slith Spear which you can take if you want.
Now head up the stairs on the eastern edge of the map to approach the main Altar. There is a large group of Troglodytes in front of the altar, as well as a few Hulking Worgs. Once you've cleared the room of enemies you can go up the ramps to the north, though none of these rooms contain anything of note. Don't approach the altar until you're ready for a large battle.
For now, go to the south now, and enter the short hallway. To the west is the room where the Troglodytes rest and wait to be blessed in front of the Altar. To the east is a small dining hall, with a Troglodyte Shaman standing behind it. Kill the Shaman, then go through the door to the east.
You don't want to read the tome in this room, since all it will do is throw fire damage at you.
Check the eastern wall near the tome however, for a secret passage. There are two more living statues just around the corner of this area. Once you've killed them, enter the small room to the north. There's a second Altar in here, apparently much more powerful than the first. I recommend dealing with this one first and then healing your party before approaching the main one.
Perform the Ritual of Sanctification and a Haakai will appear. They're rather difficult to kill, so save your game before performing the Ritual.
Once you've killed the Haakai check out the northwest corner of the room for another secret passage. There's a demon in here, guarding a chest. Kill the demon and then check the chest for a couple potions and a suit of Shadow Leather.
Heal your party up, go outside and rest if you need to, then approach the main altar. Performing the Ritual of Sanctification here will summon 2 demons, 3 Vile Imps and 4 Hordlings. Kill them all and then return to Shamirik to tell Commander Corrie you've completed her quest, then go talk to Mayor Knight, who should now give you the quest to go speak to King Vothkaro.