This quest is very simple. You have to find Esbern who can be located in the Ratway Vaults near the Ragged Flagon which is the location of the thieves guild.
Firstly you have to talk to Vekel the Man who is the bar tender of the Ragged Flagon. He will tell you that you can find Esbern in the Ratway Vaults. Follow the quest marker and interact with the door. Esbern will open the door if you tell him the right thing. He will take about half a minute to open the door. Once inside talk to him to complete the quest.
