Time to go to the cavern. From the plaza we were in the for the last quest, drop southwest into the water and locate the door leading to the Ratway. Inside the sewer, proceed and you'll find two thugs talking about the guild. You'll have to kill them, naturally. Proceed further in and when you drop down, you can go two ways. The long way to the west, or go east and try your luck opening the locked Expert door.
Either way, when going west, in the next room, you'll find oil all over the floor, so use that to your advantage. In the next room, you'll find a guy who uses fists as weapons. Kill him and beware of the bear traps inside this room. There's an Alchemy Station here, so use it if needed and proceed. From here, proceed to the little garden and in the next room, kill the thug and read the book SKILLBOOK "Beggar" on the table to have your Pickpocketing skill raised by 1. Now proceed into the Ragged Flagon.
Inside this cool looking tavern, locate Brynjolf and speak to him. Tell him you'll collect on his "Deadbeats" for him and now you got three more objectives. Ask about the other tips on each target and you'll get three more [Optional] objectives.
You can do these objectives in any order you wish. You can also either choose to take advantage of the optional objectives or not, it's really you're call. I'd take advantage of them unless you want to get into brawls with people. Also, for the love of god and all that is holy, TALK to the deadbeats before just punching them!
The objectives are as follow:
Head over to the Bee and Barb building. Speak to Keevara the Argonian and tell her you have a message for her from Brynjolf. During the chat, tell her that "Don't say I didn't warn you" to brawl with her. Beat the living lights out of her and when she's on the ground, speak to her again and she'll pay you 100 Gold.
On the other hand; if you don't wanna brawl with her, speak to the other Argonian here with the marker over his head to learn something intimate about Keerava. Go back and talk to her again and bring up her family and after that, you'll get the payment.
Step into her Bunkhouse. Same deal. Tell her about Brynjolf and then brawl with her. Afterwards, she'll get the money for you. On the other hand, if you wanna avoid brawling, go to the southeast corner and look around for the Statue of Dibella. Steal it, then show it to her to get your payment. Oh, you sneaky bastard you.
After you've collected from TWO people, the THIRD one will give you the money right away when you bring up Brynjolf's name. That's the power of word of mouth!
Bersi Honey-Hand's Debt
Head over to the Pawned Prawn and speak to Bersi. Tell him about Brynjolf and then tell him "I think you need to shut your mouth". Brawl with him and you'll get your payment. On the other hand, if you don't wanna brawl, break the vase in front of him and you'll get your money.
After you got all 300 Gold, return to the Ratway and speak to Brynjolf. He'll be pleased if you give him the 300 Gold and there were no casualties. He'll give you a Poison, a Healing Potion and Fortify Stealth Skill. Keep on speaking with him and you'll join the Thieves Guild.
Taking Care of Business
Join the Thieves Guild