While it is extremely easy to join most of the other factions within the game it can be a challenge just trying to find The Dark Brotherhood.

You can begin by speaking to the bar staff in Windhelm, who will eventually (it takes alot of pestering) tell you go find a boy called Aventus Aretino, who can be found in the Aretino household within Windhelm. Go to him and begin the "Innocence Lost" quest.

After some time a courier will approach you with a message, read it and then go find a bed to sleep in. You will then be contacted by the secret society. Be sure to speak to the stranger in the room when you wake up to confirm your desire to join The Dark Brotherhood.