After you have joined the Dark Brotherhood and completed With Friends Like These… you have to talk to Nazir about contract work. He will ask you to kill 3 different people around Skyrim. Only one of the three is somewhat difficult because it is in a built up area.
How To Kill with Stealth
Even if you are hidden you cannot use a sword to assassinate someone, nor can you use magic. In the brief seconds before their death they will notice you and you get a bounty. The only way you can perform a stealthy kill is through using a bow and arrow. I decided to use a deadric bow which you can make with one deadra hearth and 4 ebony ingots, if you want to upgrade it too. A guide to deadric armor and weapons is here.
If you haven’t done the Dawnstar museum quest speak the to guy outside the house next to Beitild’s house and he will go inside. Then you can lock pick Beitild’s house and get inside without being noticed. Beitild is only home during the night when she sleeps. I found here there around 2 am. Use a bow and arrow to kill her in bed whilst hidden, otherwise a guard will come into the house and attempt to arrest you.
Narfi is very easy to kill. It doesn’t matter when you kill him as long as you are hidden. Nobody is near where he lives, so you won’t get a bounty for killing him. I found him standing around near his hut during daytime.
Killing Ennodius Papius
Just like Narfi this guy is very easy to assassinate. I found it best to kill him at night when he is sleeping in his tent. Be sure to check that you are hidden and shoot him from a safe distance.
After you have killed any one or all of them you can return to Nazir and collect your bounty. The Dark Brotherhood Quests will only advance after you have killed all three targets.