Complete the quest “Innocence Lost” by speaking to Aventus Aretino in Windhelm and killing Grelod the Kind in Riften
Sleep in any bed after finishing “Innocence Lost”
Wait for Astrid to abduct you to the abandoned shack
Choose one of the captives and kill them
Speak to Astrid after the kill
Travel to the Dark Brotherhood Sanctuary near Falkreath
Enter the sanctuary and speak to Nazir to begin joining the Dark Brotherhood