How do you start the Dark Brotherhood questline in Skyrim?

Two ways in. Most people get it by going to the orphanage in Riften and killing Grelod the Kind, which is what a kid in Windhelm called Aventus Aretino asked for. Or wait for the rumour about Aventus doing the Black Sacrament. After the contract, sleep somewhere and you'll wake up in a shack. Fair warning, killing Grelod will get you a bounty if anyone sees, so do it quietly.