After finishing the quest Innocence Lost, wait for a courier to deliver a message from the Dark Brotherhood (if after waiting for a time the courier doesn’t appear, fast travel or take a carriage to Falkreath, which is the closest city to the Dark Brotherhood’s headquaters - he should appear sometime after that). Then go to sleep in any bed for any amount of time.
when you awake, you won’t be where you were when you went to sleep; you’ll find yourself in a shack with a bunch of strangers. A hooded woman known as Astrid tells you that she is from the Dark Brotherhood and that you apparently owe them a debt. To repay this debt, you need only kill one of her three captives - the other people in the shack with the two of you.
Choice 1) Submit to the Dark Brotherhood
If you talk to the three captives, whether through basic interest or to try and discover which one of them has a contract out on them, you will discover that one is a mother of six, the other a soldier and another a Khajiit who is the authentic target with the contract on his life.
Kill the Khajiit or kill all three of them to impress Astrid. After you’ve done the deed, she will extend you an invitation to join the Dark Brotherhood. She gives you a key to the shack so you can let yourself out, and urgest you to come and find her at the Dark Brotherhood headquaters near Falkreath. When/if you decide to join, walk up to the creepy-looking door and respond to the question with “Silence, my brother” to be granted entrance.
Speak to Astrid to receive your welcome package for officially joining the Dark Brotherhood and end this quest.
Choice 2) Resist the Dark Brotherhood
If you refuse to submit to the will of the Dark Brotherhood and kill one of the three captives, then to escape from the shack with your life you will have to fight and kill Astrid.
If you manage it, you will find the key to the shack on her body. The quest for the Dark Brotherhood will come up as failed in your quest journal. The Dark Brotherhood questline now over until a new quest titled “Destroy the Dark Brotherhood” is received. You are now able to set the three captives free and are advised to inform a guard of Astrid’s death.
You can walk up to any the guard in Skyrim and tell them of Astrid’s death. Solitude is the nearest destination to the shack and there are plenty of guards there. After you have informed a guard, they will tell you to find a general at Dragons Bridge and inform them of what has happened – impressed that you were able to take down the leader of the Dark Brotherhood.