Start by following Brynjolf and once in the Cistern, you’ll get together with Mercer Frey, the Guild’s leader. Talk to him and he’ll give you a job to do to prove your worth: you need to go to Goldenglow Estate and burn a bunch of beehives and clear our Aringoth’s safe. Be sure to ask Mercer all the questions you can to get all the optional objectives.
Also, speak to Torilia to know that she’s the Fence down here. You’ll want to get to know her really well, as she can buy your stolen items from you and lord knows that means something!
After some chat, you’ll receive a complete set of Thieves Guild Armor. Nice. Put them on if you so desire. Return to the Cistern and head out of Riften. You can enter this place one of many different ways. You can use the sewer Vex told you about (get to it by going to the dry land north of the lake and coming in by the south; it’s the middle objective), or you can just go through the main gate, slaughtering all the mercenaries. Either way, let’s continue once we’re inside.
On the southwest corner of the isles, you'll find 5 beehives. The objective states that you should only burn 3, so do so. Some mercs will show up, so deal with them if you want to and proceed to the northeast island, where the Goldenglow Estate is. Go inside by either entering from the front which is unlocked or by the back (a more sneaky option) which has an EXPERT lock and an [Optional] objective pops up: Obtain the key to Aringoth's safe.
Inside, sneak your way/kill to the east side of the Estate, which has a locked gate and some stairs going up to the second floor. Go up to the second floor and make your way around this maze-like floor. Loot all the rooms and when you get to Aringoth’s, either pickpocket the key from him, persuade him, or fight him.
Either way, when you get the key, return downstairs and go down to the basement and here, sneak your way to the marker and open the safe. Take the loot inside, then go into the sewers right next to the safe to make your escape. After that, head back to Brynjolf and speak to him. Show him what you found and in the end he'll pay you your pay (600 Gold) and will tell you that Maven Black-Briar wants to speak to you personally.
Skyrim is the homeland of the Nords, a fierce and proud warrior people who are well suited for the bitter cold and mountainous terrain which defines the land. Now scarred by civil war, Skyrim faces its darkest days with the return of the legendary dragons and their leader, the World-Eater Alduin. The future of Skyrim and even the lands beyond hangs in the balance, as the people await the prophesized Dragonborn, a hero born with the power of The Voice and the only one who can contend with the dragons. You are that Dragonborn; your task is to investigate why the dragons are returning, and discover a way to defeat them. At the same time, you’re free to explore Skyrim at your own pace, uncovering its many wonders along the way.