Affairs of a Wizard
Your first drop is on Hero Hill. If you've completed the Fighters Guild mission, "Mystery at Harlun's Watch," or the Mages Guild quest, "Vahtacen's Secret," you've got a couple of nearby landmarks (Swamy Cave and/or Vahtacen). Hero Hill is a steep climb northeast of those two. If neither of them are on your map, travel south-southeast from Harlun's Watch (which should be on your map; it's just outside of Cheydinhal) until you get to the river and then approach Hero Hill from the southwest. The climb is very steep, though. You'll find your instructions in a hollowed out rock near the top step.
You're to kill a Necromancer named Celedaen, who is at Leafrot Cave and trying to turn himself into a Lich (what is it with Mages and the immortality thing?). Your orders tell you that Celedaen is too powerful to face directly, but suggest looking through whatever writings you find in the Cave for a weakness that you might be able to exploit. Necromancers may have a thing for immortality, but they are still Mages at heart and like to write things down. Leafrot Cave is way south of you and, unless you've been doing some exploring on your own, you'll probably have to hoof it most of the way.
Once you're there, you'll find almost everything you need (except Celedaen) in the first big room. Read his journal, The Path of Transcendence, which is on the desk. Is it just me or does anyone else think that really powerful wizards and Lich wannabes should be able to afford better quality Alchemy equipment? I mean, really. Novice-level stuff? Anyway, after reading the journal you'll get a journal entry of your own to the effect that perhaps pickpocketing the wizard's special hourglass would do the trick.
Now Celedaen is a Necromancer, so be prepared to deal with several of his leveled undead while you're working your way back to him. Unlike a lot of the caves, forts and ruins, Leafrot Cave's shortcut makes it easier to get to the target, but it's a long walk back. If you choose not to use the nearest door, it will be a long walk there and back out again.
If you use the door in the room with the desk you'll be able to enter Celedaen's section of the caves in a more or less deserted area. There's a hole in the floor which you might be able to use to snipe him from above, but don't count on it. You'll probably have to drop through to to get to Celedaen. Find a dark corner somewhere, stealth yourself, and wait for him to come wandering by so you can pick his pocket. He'll make a little "oomph!" sound and collapse. Your mission is complete. Well, except for getting out again - no Levitate in Oblivion, remember? You'll have to take the long way. Watch out for undeads and you'll be OK.
Your payment and the location of your next dead drop are in a sack behind a bush next to the big tree in Chorrol.