Upon first entering Khoth's lair from the outside you should just make your way to the slope leading down to Sulfras, since you won't be able to enter Khoth's chambers until you've spoken to Sulfras. Once you have, return to Khoth's lair and go through the portcullis' in the southeastern corner.
There are lots of bookshelves in Khoth's rooms, many of which have something useful to teach, but there are three that you should avoid. In the northwest corner of the lair the northernmost of the short bookshelves gives you Dread Curse, and the next row south has a book that will cause Dumbfounding. On the other side of the lair, near the entrance to Khoth's room is another group of bookshelves. The northernmost of these will teleport you into one of the lava pits at the entrance. Other than those three just walk along the bookshelves to learn a variety of useful things.
Khoth himself can be found in the northwest corner of the lair, and besides telling you to find the ritual Sulfras sent you for on the bookshelves, he also teaches some spells. Once you've been inside Footracer Province come back and speak to him again to get Arcane Summon Lv.3.
Along the southern wall, near the doors to Khoth's room is a secret passage leading in to a small library, but unfortunately you can't approach the bookshelves or see what's in there due to a magical barrier that has been put in place.
Make your way to the southwest corner of the map until you find yourself in a long hallway going east/west with lots of doors. Each door leads into a cell with some of the monsters that have been plaguing the different areas.
Once you've finished in here either go to Athron's Lair, either through Sulfras' Lair or around the mountains on the surface, or return to talk to Sulfras if you already got the metal from Athron.