Sheogorath

Sheogorath's shrine is fairly tough to find, especially since there aren't any characters in the game who'll actually tell you where it is. It's south of Bravil, halfway between Bravil and Leyawiin. If you follow the road south of Bravil, the road will eventually make a small C shape on the map after crossing a river. Immediately to the south of this twist is Fort Nomore, to the southwest of Nomore is the Shrine of Sheogorath, near the border between Cyrodiil and Elsweyr.

If you speak to the characters around Sheogorath's shrine, you'll discover that most of them are...well, pretty damn crazy. One of them, at least (in the white robe) will be lucid enough to tell you what to offer Sheogorath's shrine to make the god speak to you: a bolt of yarn, a head of lettuce, and a Lesser Soul Gem. None of these should be particularly difficult to find. If you head to the Imperial Market District, you should be able to buy lettuce from the Feed Bag, the soul gem from the Mystic Emporium, and the yarn should be findable in plenty of basements or warehouses. You might want to check in the basement of ....

When you do manage to summon Sheogorath, his quest will involve travelling to the hamlet of Border Watch, a bit to the south of the shrine. When you arrive, speak to Ri'bassa, the town's shaman. He'll tell you of three prophecies: one involving a plague of rats, one involving the death of the town's livestock, and one which he doesn't consider fit for outsider's ears. Note that you need to have a fairly high disposition with Ri'bassa to hear the specifics of the prophecies; you can help this out by telling him that you're a travelling scholar, then either speechcraft him or bribe him up over 60 or so to get the specifics on the plagues. Also ask him about the town for hints as to what you need to do.

Poison the sheep and cause a rat stampede to wipe the town off the map!

To start the plague of rats, you'll need to steal an exceptionally stinky wheel of cheese from the Border Watch Inn. It's in one of the locked display cases here; it's the larger orange wheel of cheese that's in its own display case. To get it out, you'll either have to pick the Very Hard lock, or pickpocket the key from the innkeeper, preferably while she's sleeping. Either way, you're going to have a hard time of this objective if you haven't been increasing your thieving skills.

When you do have the Olroy Cheese, though, head outside and place it in the melting pot near the top of the stairs in the middle of town. Wait for a few moments, and there'll be a rat parade! Hooray! You can help kill the rats, if you wish, or just watch them scamper about for a bit.

If you wait for a few hours, a pile of rat poison should appear in the middle of the town's central staircase. Grab it and head to the southern part of town where the sheep are corralled. Put the poison in the feeding trough to kill them all off, and Sheogorath will tell you to visit the center of town. When you do, he'll initiate the Plague of Fear by himself...and let loose a hail of dogs onto the town. Dogs on fire. Dead dogs on fire. This game is pretty weird at times.

Anyway, after successfully freaking out the entire populace of Border Watch, return to Sheogorath's shrine to obtain the Wabbajack, a staff that can turn any creature into any other (random) creature. You can't choose its effects, but it can occasionally make difficult fights much easier, such as by turning an incredibly difficult enemy into a Rat or something similar.

Vaermina

Vaermina has one of the more difficult tribute requests to fulfill, despite the fact that you can do this quest as early as level five: she needs you to bring her a Black Soul Gem. Finding one of these is going to be a quest in and of itself for most characters.

Obtaining a Black Soul Gem Black Soul Gems are necromantic tools, used when a necromancer wishes to capture the soul of a humanoid character. Normal soul gems can only capture the souls of creatures, but a black soul gem will let the user capture the soul of a human - definitely not something you're going to need very often, unless you're something of a badass. Anyway, in order to find one, you'll have to deal with necromancers, which can be found in their own special lairs, as well as in some of the other quests you may have to deal with.

If you want to obtain one of these gems early on in the game, then you should attempt to do some of the Mages Guild quests - one of the recurring themes of those quests revolves around the Guild's attempts to root out and destroy necromancy. If you can't find one that way, though, you can occasionally find Black Soul Gems on the bodies of necromancers, but this is unlikely to occur before you're level 15 or so.

Find one of these altars to make your own Black Soul Gem.

Another way to acquire a Black Soul Gem is to make one yourself via the shrines outside of necromancer strongholds. To do so, you'll have to have a Grand Soul Gem (which you can buy from merchants in most Mages Guild halls, or steal from the Chorrol Mages Guild. When you have one, as well as any level of Soul Trap spell, head out to a necromancer stronghold with an altar outside of it, such as Fort Linchal, which is northeast of Kvatch, just north of the "H" in "Kvatch" on your map.

When you find an altar, start waiting in 24-hour increments. Each altar will have one day of the week when it's powered-up, which is indicated by a beam of light that shines down from the heavens. When you see this beam of light, place the Grand Soul Gem in the altar (making sure it's empty), then cast Soul Trap on the altar to obtain your new Black Soul Gem.

The Quest Itself When you've delivered the Black Soul Gem to Vaermina's Shrine, she'll tell you what she wishes you to do. She'll tell you a tale of the Orb of Vaermina, which was stolen from her by the wizard Arkved. Find him, retrieve the orb, and return it to her for the reward.

Arkved's Tower is a short walk from the Shrine of Vaermina. Although it appears to be just another Fort, you'll find that the interior has a more....deliberate layout. Arkved is apparently either insane or very eccentric, because you'll find rooms that are completely upside down, rooms that are populated by Daedra, and so on. Make your way into Arkved's Lair for the ultimate mind-trip: it's a room that apparently obeys none of the laws of spatial interiors.

Arkved's dreamspace is a pretty disturbing place to dwell in.

Pass through into Arkved's Lost Halls and find the exit to the Hall of Changes. (Arkved's Oasis is apparently a dead-end.) Follow the red compass pointer until you reach the trap door to Arkved's Rending Halls. (The Retreat is also a dead-end.) Fight your way through the Halls to the Death Quarters, where Arkved lies sleeping.

The Orb of Vaermina stands on a desk nearby, near the Palla, Volume I book, which will increase your Illusion skill by one point. Grab it, then sneak out the door nearby to return to the "real world." You can kill Arkved if you like, but he doesn't offer any decent loot. With the Orb in hand, return to Vaermina's Shrine and offer it to her. She'll give you the Skull of Corruption, a very fun little toy that will make a clone of anything you aim it at. This includes people, but note that using it against regular civilians is considered a crime, due to the fact that the clone will always attack the original.