The Skulls

The first part of this section involves a room with eight doorways and only one of them leads out (kind of hard to get lost with those odds). There are a few critters (usually Vampires) behind three of the doors. There is a cage behind one of them and clicking on the door opposite the cage will teleport you into the cage, which will descend into a room with four orcs in it. If you really feel like exploring, anchor a "recall" in the center of this room and start opening doors. If you get teleported into the cage, cast "recall" to get back out again.
Once out of the room, follow the corridor. There will be a passage to the right a little way down the corridor. This leads to the room with four orcs in it (and there's usually a minor critter of some kind waiting at the first corner). If you follow the corridor until it T's and go right at the T, you'll come to the room with four orcs. You need to turn left at the T and go through the door to get the the next part. The little north-south hallway is a safe place to rest if you need to.
There are four Fire Daedra on the floor of the chamber and one in one of the eyes of the central skull. Unless you really like being fireballed when you're not looking, it's probably a good idea to drop down to the floor and dispatch the Fire Daedra. Click on the cage and you'll be teleported back into the little north-south hallway. There are a bunch of fire atronachs on the walkways.
Go west along the path until you get to the first floating skull. Look up and click on the skull. It will give you a clue (something about all true followers lifting up their eyes, etc.) and start turning. If you paid attention to the clue, you should have a good idea that you're looking for skulls that face the big center skull. There are only two. Continue west until you get to the next skull, click on it and it will start turning. Go back to the intersection of the paths and go south. Start counting skulls. When you get to the third skull, click on it (it starts turning) and keep going along the pathway until you reach the end.
The fifth skull faces away from the big one. Clicking on it will cast "Heal" on you, but it won't turn. The rest of the skulls will either just start turning or will teleport you elsewhere in the chamber (usually right next to a small skull with nothing under your feet). There's a Fire Daedra in the right eye socket of the big skull. A bow shot will usually knock him off and he'll drop to the floor. Levitate over to the chamber behind the eyes of the skull (I've never been able to successfully jump, regardless of how high my stats and jumping skill are).
In the left eye socket (as you're facing the skull), you'll find Sheogorath. Talk to him if you want. Nothing will happen to you.
The tricky part is the elevator inside the room behind the eye sockets. It goes up and down as you walk on the floor of the chamber. Since you probably have a "Levitate" active, step on the floor to make the elevator descend and then float over to the shaft and go down. There's a room with a large stone head at the bottom. You'll have to crouch down to get through the doorway. When you click on the head it will ask you, "how many defy me". Answer, "One" (the number of skulls facing directly away from the big one). This teleports you to a chamber with skulls on the shelves, which is the beginning of the next section.

From Jormungandr (16 March 2006): [other than jumping into the big skull's eye rather than levitating (as the guide suggests), this is also no different than normal.]