Scheduled for Execution

Background
Vicente asks you to kill a prisoner, Valen Dreth, who is soon to be released from prison. The bonus is not to kill any guards during the course of the mission.

Walkthrough
First, enter through the Imperial Prison Sewer, where you exited the character creation tutorial. Open the gate with the key you were given by Vicente.

Once you are in, go to the tunnel to the right from the entrance and continue through the sewers through another door to more Sewers. Pull up your map and follow the pathway to the red triangle. There are 2 locked doors. Both of them are Average locks.

Go down the stairs and go right through the gate, down the hallway, and then make another right at that room. Make yet another right down the hallway, up the stairs, and up the ladder to The Sanctum (the locks difficulty depennds on the pc current level at level 5 its an average lock). Either use a lockpick, or use an Open Hard Lock spell. In order to use the spell, you need to be at least 75 skill points in Alteration magic. If you don't have the spell, you can purchase it from Gaspar Stegine or Raminus Polus in the Imperial City Arcane University, or from Orintur in the Cheydinhal Mages Guild.

There will be guards in the next few areas. The sewer network is dark, and the guards seem to have a low detection range, so even a character with relatively low sneak skill can evade them as long as they stay in the shadows, and avoid line of sight. The guards will move around their posts a bit, but sometimes you need to have a lot of patience.

Once inside, sneak and wait for the two guards to stop talking and walk away. This conversation is worth hearing at least for the humour, and it only takes around half a minute. There are now two options: either sneak forward or to the right. If you go forward, you will have to evade several guards, however you can access the chamber through which the assassin (remember the tutorial?) jumped out of to attack the Emperor. This chamber is now lit by candles and leads to a sort of shrine to the Emperor in which the guard captain in charge of the site has set up his office. He is engrossed in whatever he is doing at his desk, and so will rarely notice you stealing his keys. These keys open doors to all sorts of restriced areas across the imperial city, and so are worth having. The other option is to sneak forward down the hall. Walk instead of running. Make sure to stay in the shadows. You’ll need to go left but a guard patrols that walkway. You will come to the area where the final ambush occurs in the tutorial (the one where the gate is locked from the other side, forcing you to detour). There is a guard stationed at the staircase you need to go up, but he can be evaded with relative ease provided you stay to the shadows and avoid his line of sight.

Then simply go through the door to the Imperial Subterrane. There is one guard patrolling this area and he's carrying a torch. Avoid him in the shadows until he passes you by, then make your way to the Imperial Prison. Go straight up the stairs and down the hall, make a left, up some more stairs turn around to the right, and go through the tunnels directly into the prison cell where you started the game.

A guard and prisoner will be talking just outside of your cell. That prisoner is Valen Dreth, the Dunmer you were assigned to kill. The guard will speak to him for a short while, with Dreth's taunting voice reminding the guard that he will be gone in a few days, while the guard will still be stuck in 'this hole'. The guard will leave when the conversation is done, leaving Valen Dreth alone. Just casually open his cell and kill him. If the player character decides to converse with Dreth, they may repeat Dreth's taunt from the beginning of the game, "You're going to die in here," or mention that the Night Mother sent him, to which Dreth will respond "The Night Mother? Oh.. No! Guards! Guards! Assassin!," hinting that he was aware of the possibility of an assassination attempt. Kill him in whatever manner you see fit, but be sure to do it quickly or he can run back through the entire sewer, leading to the guards noticing and attacking you.

After Dreth is dead, you can either exit through the sewers, or you can take the key on the table (left of the cell you enter from, right from Dreth's cell) and exit through the Bastion. The guards there will not be hostile, and this route is much faster and safer.

Alternate methods
Instead of attempting to sneak past the guards in the sewers, you can also pickpocket one of them for the Imperial Prison Key. After obtaining it, you can then exit the sewers, enter the Imperial Prison from the front door, enter the Bastion, then go down the left door that says it requires a key to unlock. (This does not work on the Xbox 360 version and possibly the PS3 version) You'll come out right next to Valen's cell with a single guard between Valen and your blade. Be warned: This guard will not move. You will have to run past him, kill Valen, and exit as quickly as possible.

Alternately, allow the guard to see you and attack you. Then yield to him by holding block and talking to him. He will stop attacking you, allowing you to initiate the conversation with Valen. After he leaves, you are free to kill Valen.

You can also just run straight past the guards - they're not that tough, and you don't bump into one until you get out of the sewer. Follow the red arrow, kill Valen as quickly as you can, ignoring the guards, and run like hell back out again, still ignoring the guards even when they hit you. Get the magicka boost from the Ayleid well just outside first to make this a lot easier, you can then cast more heal spells as you run through the sewers. Once you get out into the open, jump straight in the lake in front of you and swim away, you lose them pretty easily and can jump back to 'base' once you reach the far shore.

Lastly, you do not need to open Dreth's cell door. Both arrows and spells can be shot through the door, and as Dreth cannot open it or attack you, all he can do is stand there and die.

The method (well, muck up) I used is to anger the guards. Then you run past his cell. While taunting you, the guards swing their swords madly. This can hit Valen and so the guards kill him-not you.

The easiest alternative to do this without *anyone* spotting you at all is this: Buy Deathly Visage (an invisibility spell) from M'raaj-Dar in the Dark Brotherhood Sanctuary early-on, and make sure your alteration skill is high-enough to use it) and then as soon as you've just exited the sewers and enter the sanctum (where you hear the guards complaining about having to guard the place), cast your invisibility spell and afterwards run past the guards before they've even finished their conversation. They won't be at their posts and you get to the next area unimpeded anyway. You are not noticed even running so no need to be in sneak mode when invisible. The spell will only last about 35 seconds so you must be quick. Run straight ahead into the darkened room, turn left and up the small ramp leading to a small set of stairs and beyond it, the door to the next area. There will be another guard, so re-activate your invisibility and just run past him into the next area. No need to use spells anymore because you are now free of enemies until you get into the cells where Valen Dreth is incarcerated.

Trivia

 * When you are accepting this contract from Vicente, he makes the comment "I think you know the way?" implying he knows you are the escaped prisoner.