This page of the guide to The Elder Scrolls V: Skyrim includes the beginning of the walkthrough for the main quest A Cornered Rat. The protagonist must meet Brynjolf and figure out where Esbern is hiding.
New main objective: Talk to Brynjolf
Open the world map and you will note that Riften is in the south-east part of Skyrim (screen above). If you have already visited that area, it of course would be best to use fast travel. Otherwise, you will have to plan your journey there. The easier solution is using the carriage, for example the one stationed in Whiterun Stable. If you want to reach Riften on your own, it would be best to start at Ivarstead, heading east and making use of the road signs on your way.
Regardless of the chosen method, you need to approach the city from the northern side (screen above). During the first attempt of entering Riften you will be stopped by the Riften Guard. You can either pay the fee for accessing the city or use Speech to convince the guard to your rights or intimidate him. Afterwards, head to the big gate to enter the city.
The person you can ask for Esbern is Brynjolf. By daytime you can meet him on the town square and during the night he can be found in The Bee and Barb. Talk with him (screen above). If your Speech skill is developed enough, you can use persuasion and convince him to give you the whereabouts of Esbern (screen above). Otherwise he will ask you for a favour. You will have to steal a ring from Madesi and afterwards put it into the pocket of a certain trader Brand-Shei. Those activities are a part of A Chance Arrangement side quest, in a way of exception described in the main guide. Of course if you already worked with the Thieves Guild in the past and completed it, you won't have to do anything and will learn where to look for Esbern at once.
Side quest unlocked: A Chance Arrangement