Starting Innocence Lost
There are a couple of ways of starting this quest. The way I did it was that I eavesdropped on a conversation about Aventus Aretino trying to contact the Dark Brotherhood. To find these conversations you have to be in Windhelm. Walk around and listen to conversations, eventually you will find one.
Killing Grelod the Kind
You can also go to the orphanage in Riften and kill Grelod the Kind. You have to do that anyway if you start the quest the way I did it. You won’t get a bounty for killing her, but you will get a bounty if you decide to kill her helper, which I did. Because I was a member of the thieves guild I paid the guard off.
After you have done the deed return to Windhelm to Aventus Aretino to finish the quest. The first time I did this quest I went to a bed and slept there and was woken up by a woman asking. That doesn’t always happen. If you don’t get woken up eventually a courier will give you a letter. read that letter and you will start the process of joining the thieves guild.
I highly recommend watching the video I linked below, especially if you are having trouble with this quest. It shows all the steps involved, but it is also a great entertainment piece.