Go to the statue of the Lucky Old Lady in Bravil and activate it to speak to the Night Mother. She will give the name and location of a client who is always outside Cyrodiil, and thus inaccessible to the Hero.
Head back to the Dark Brotherhood Sanctuary and tell Arquen. She will pay a share of the Brotherhood's earnings for the week, about 200 .
This quest can be completed an unlimited number of times, once every week and will cause Dark Brotherhood Murderers to start appearing in Cheydinhal Sanctuary, where they can be recruited as followers. More will appear as the quest is completed repeatedly.
Once a week, I must speak with the statue of the Night Mother in Bravil. The Night Mother will give me a list of names and locations of people who require a visit from a Dark Brotherhood Speaker, to arrange an assassination. If I take this information to Arquen in the Cheydinhal Sanctuary, she will give me my weekly earnings. I can do this every week for as long as I want, and there is no penalty if I choose not to.