Make your way to the Ratway. To do this, go over to any of the bridges and drop down to the pier area below. Just follow the piers and behind a gate is the door for the Ratway.Inside the Ratway, you'll find a few hostile bandits. Kill them and head to the bigger room. Head out of the room to the west and light the floor on fire because there is oil all over it. Turn left. You will enter a room with a rather large man. Kill him but watch out for the bear traps on the ground. Once he's dead, go past him and eventually up some stairs. Cross through the garden and in the next room you will be able to see the door for the Raggad Flagon.
Brynjolf will instruct you to collect debts from three business owners.
Speak to the male Argonanian Talen-Jei about talking some sense into Keerava. Then Talk to Keerava to convince her to pay.
Steal the state around the corner. Be careful because you can still be caught. Once you have it, talk to Haelga to get her to pay up.
Attack the urn in front of him until it breaks, then talk to him to get him to pay.Go talk to Brynjolf and he will introduce you to Mercer and you will be welcomed into the guild.