The Lonely Wanderer
Your first contract for Ocheeva starts out inauspiciously. You're to assassinate a High Elf named Faelian who lives somewhere in the Imperial City and likes to take long walks. As if the almost complete lack of information weren't frustrating enough, you need to do it in such a way that Captain Adamus Phillida of the Imperial Legion has no reason to suspect that the Dark Brotherhood was involved. This means that the assassination needs to be done quietly, privately and with no witnesses.
It's time to poll the Sanctuary. No one except Valtieri offers much in the way of useful advice. Valtieri's information is not advice so much as it's an observation that the elven community in the Imperial City tends to be rather tight-knit; everyone knows everyone else. So, armed with the loads of information you've been given, off to the Imperial City you go. Ask any High Elf with a Disposition of 50 or more about Faelian and you'll be told that he's a "rather distateful fellow" who lives at the Tiber Septim Hotel in the Talos Plaza District. Thieves Guild members take note: the beggars can't help you with this one. You have to talk to High Elves. Or, if you've got a real set of cajones, ask Adamus Phillida about Faenlin. He'll give you the same repsonse as the High Elves and direct you to the Tiber Septim Hotel.
Your options at this point are rather limited. You can stake out the Tiber Septim Hotel in the hope of catching Faelian as he enters or leaves (he won't talk to you in the hotel, so this has to be done outside). He comes in about 8 p.m. and leaves again about 1 a.m. Alternatively, you can wander around the Imperial City looking for him. This is a bit more difficult than it sounds since you don't know much about his habits. However, since I've done all of the footwork for you, you'll know that he hangs out in the Abandoned Shack in the Waterfront from about 2 a.m. until 8, then he wanders over to the Elven Gardens district where he wanders around until about 11-ish when he goes into Lorkmir's house and stays until about 5 p.m., then he wanders around Talos Plaza until 8 when he goes into the Tiber Septim and repeats the process.
If you do manage to find and talk to Faenlin outside the hotel, it will be pretty obvious that the guy's lost it. He wants skooma and that's all he wants. If you have some skooma, he'll be your bestest friend in the whole wide world. So where to get some? A few places come to mind. First off, there's Lorkmir's house (break in and there are three vials on the table). Then there's the Skooma Den in Bravil (there's a locked chest with three bottles). There is a locked barrel near one of the houses in the Waterfront that occasionally has some skooma in it. There is a skooma dealer just outside of Leyawiin that you have to take care of in a Miscellaneous Quest ("Raid on Greyland") who has three bottles in a chest. It also occasionally turns up as leveled loot. If you have some skooma and give it to him, he'll tell you about his "special place" at Lorkmir's house, give you the key (saving you the trouble of breaking in), and ask you to come by after 11.
The better approach is to talk to Augusta Calidia, the blonde Imperial behind the front desk. With a Disposition more than 50, she'll tell you all about Faelian and how he's living off of his girlfriend, Atraena, and how he has a skooma problem. If her disposition is between 30 and 50 she'll tell you that she knows something, but hardly knows you. Less than 30? Fagedaboudit. Once you know about Atraena, you'll get a pointer for her. She's upstairs. Since she never leaves the hotel, she should be very easy to find.
Atraena, if her Disposition is more than 50, will tell you how he walks around the city looking for skooma and then spends a few hours in Lorkmir's house in the Elven Gardens district, which she thinks is deserted. Aha! A solution begins to present itself and you don't have to come up with any skooma. Break in to Lorkmir's house, wait for Faenlin to show up and kill him. It's private, quiet, and just about everyone is expecting that the skooma will kill Faenlin, anyway.
If you search Lorkmir's house, you'll find Lorkmir's body in the basement. But the house is otherwise deserted and ransacked, so it's the perfect place for your assassination. Kill Faenlin when he shows up and you're done. You're never told who wants Lorkmir out of the way or why, but the list of suspects is pretty short: Lorkmir's relatives or Atraena's parents. No one else has anything to gain by it.
Report back to Ocheeva for your payment and the enchanted bow, Shadowhunt. It has a leveled Damage Health, Damage Magicka, Turn Undead and Weakness to Poison enchantment on it. If you failed Valtieri's last contract, you'll get your promotion and the key to the Sanctuary now. Sadly, no one has anything to say about Faenlin afterward. Even his girlfriend doesn't notice that he's gone. Stay away from Skooma, kids.