Location: on the eastern shore of Lake Poppad (link goes to the Daedric Shrines map at UESP Wiki)
Minimum Level: 5
Offering: Black Soul Gem
Reward: Skull of Corruption
Objective: retrieve the Orb of Vaermina from Arkved's Tower
This shrine can be marked on your map by Ontus Vanin in the Talos Plaza District of the Imperial City. It's not hard to find, though. I usually stumble over it rather than have it marked. Start at Cheydinhal and travel southwest to Lake Poppad (it's on the eastern shore), start at Vahtacen (Mages Guild quest location) and travel west-southwest, or start at Muck Valley Cavern (Dark Brotherhood quest location) and travel northeast to the other side of the lake.
Since the quest becomes available at level 5, the hard part is going to be finding a Black Soul Gem for the offering. They just aren't very easy to find at level 5.
Perhaps the easiest way is to simply make your own. Travel to either Dark Fissure (up in the mountains south-southeast of Cheydinhal - it's marked on your map for the Mages Guild's "Necromancer's Moon" quest), Fort Istrius (just off the road between Kvatch and Skingrad, kind of southeast of the Rasava bandit camp), Fort Linchal (northeast of Kvatch and northwest of the Rasava bandit camp), or Wendelbek (between the two northern branches of the Panther River). Outside of each of these locations is an altar. Once per week it has a purplish light shining down on it. This begins at midnight on the appropriate day, so you might have to wait as long as six days before it happens. While that light is shining on the altar, put an empty Grand Soul Gem into the altar and cast "Soul Trap" on the altar. You now have a Black Soul Gem.
You can sometimes find them as loot in Necromancer lairs, but they usually don't start showing up until you're somewhat higher than level 5. I'm only aware of one guaranteed find of Black Soul Gems: the Cheydinhal recommendation quest for the Mages Guild. When you complete the quest and search Falcar's quarters, you find two Black Soul Gems. You only need to turn over one of them to complete the recommendation quest. The problem is that the second one will be removed from the game when you do that. So you'll need to make the offering between the time that you pick up the Black Soul Gems and the time when you turn them over to Deetsan and complete the recommendation.
So, if you're at least level 5 and have not completed the recommendation quest for the Cheydinhal guildhall, start the quest and get to the point where you find the Black Soul Gems in Falcar's quarters. Take one of the two that you find and go to the shrine where you use it as the offering. This will start the quest and get Arkved's Tower marked on your map. Now you can either go back to Cheydinhal, collect the remaining Black Soul Gem and turn it in to complete the recommendation quest or you can continue with Vaermina's quest and complete the recommendation later.
Arkved has stolen the Orb of Vaermina and Vaermina very much wants to have it back. Arkved's Tower is south-southeast of the shrine and not very hard to get to. Once you're inside, however, it's another story. The place is crawling with leveled Daedra in some places, while others are almost completely deserted. All told, there are seven levels to the tower and Arkved is on the last (isn't it always like that?). The tower is something out of a dream or nightmare with rooms with giant furniture, rooms with furniture on the ceiling, passageways that go nowhere, doors that open onto blank walls; Freud would have a field day. You do not, however, have to do anything to Arkved when you get to him. He's in his bed, unconscious. You can kill him if you want, but it's not necessary for the quest. He's left a few notes laying around that you can read to get an idea of what's going on. While you're at it, pick up Palla, Volume 1 (Morrowind players may remember it - it boosts your Illusion skill) because it's the only copy in the game. And don't forget to pick up the Orb of Vaermina.
The trapdoor in the northeastern wall will put you outside of the tower. You can now return to the shrine and collect your reward: the Skull of Corruption. It creates an "evil twin" of whatever you blast with it, so it can be very useful against higher-level opponents. Tricksters beware: using the Skull on NPCs is a crime. Killing the clone, though, is not.