Join the Dark Brotherhood after I got attacked by one of their Assassins

It's a random encounter for you to get to know there is an Assassins Guild in the game. It happens always early in the game (so it's somewhat scripted) and later you get the option to join them or destroy them.

The player never gets to know who wanted you dead and you can't ask any of the Dark Brotherhood about it. It's not really that important.

Assassins will keep being sent by Astrid until you join the Dark Brotherhood, so if you want to stop getting assassins hired, join the Dark Brotherhood.

From the Yahoo! Answers post, "How do i join the dark brotherhood in skyrim?":

While on your travels in Skyrim, go to any inn and ask for the latest gossip. The innkeeper will tell you that there is a child trying to perform the Black Sacrement in Windhelm. If you happen to be in Riften, speak to a man named Maul. He will be standing against a post as soon as you enter the city. After sharing some tough words with you, he gives you information on both the Thieves Guild, and the Dark Brotherhood; for a price, of course. You could alternatively talk to Idesa Sadri inside Candalhearth Hall in Windhelm and ask about a cursed child performing the Black Sacrement. Idesa can also be overheard talking to Grimvar Cruel-Sea about the child, Aventus Aretino, outside the Aretino Residence. Aventus Aretino can be found inside the Aretino Residence, which has a novice-level lock. The child will offer you the Innocence Lost quest, which will lead to the quest With Friends Like These....

After Innocence Lost has been completed, a courier will appear and give you a note with the imprint of a black hand and the words "We Know" written beneath it. If you do not receive the note, wait for a couple of days. Once you receive the note, sleep in any bed. Thereafter, you are abducted by the Dark Brotherhood, taken to an Abandoned Shack, and asked to kill one of three people in the room (With Friends Like These... ). Killing one or all of the potential victims will earn you an invitation to join the Dark Brotherhood. You may also take the opportunity to destroy the organization by attacking the Dark Brotherhood representative, Astrid. This will initiate the quest Destroy the Dark Brotherhood!.