New main objective: Follow Brynjolf
New main objective: Listen to Mercer Frey
After you finish Taking Care of Business, Brynjolf will start trusting you and decide open the secret passage to the Guild headquarters, the Ragged Flagon Cistern. Follow the quest giver. Listen precisely to what the Guild leader - Mercer Frey - has to say, as he will give you many valuable information.
New main objective: Talk to Brynjolf
After listening to your new boss' tirade, speak to Brynjolf - he will order you to break to the Goldenglow Estate and burn three bee hives found there. Getting inside is quite hard, though if you speak to Vex she should show you an easy passage through the sewers.
Before moving on to this mission, use up all dialogue options with Brynjolf - that way you will not only get some useful tips regarding the quest itself, but also additional mini-missions.
Before leaving The Ragged Flagon, speak with the character inside - some of them might teach you something, other (like Delvin Mallory or Vex) will offer additional missions. Once you're ready to head outside, go to the secret passage found in the south-east corner of the Cistern (a ladder visible in the screenshot above).
Goldenglow Estate, to which you have to break in, is found in the middle of a lake slightly west of Riften. In order to reach the island, you will have to use the sewers entrance marked on the map by Vex. Before heading out, make sure you have something to set fire to the hives with - either a torch or a fire spell. Both can be easily found throughout Skyrim, as well as bought from merchants.
If you prefer more invasive methods, there's no problem - instead of going to the sewers below the estate, you can just kill the guards by the entrance gate and take their keys. It's however a solution meant for characters who can fight - the guards are rather strong. If you decide on such an option, skip to the Clear out Aringoth's safe section.
New optional objective: Enter Goldenglow using sewer
If you like more stealthy gameplay, it's very important that you head out during the night - it will increase your chances of staying unnoticed. After swimming to Goldenglow Estate, enter the sewer - the hatch is in the northern part of the location (see screen above). After getting down, you will have to fight a few Skeevers - they however aren't very demanding enemies.
You should note that at some point, a weird orange substance will start appearing on the floor. It's very flammable, so look out no to get hurt. It's however a good idea to set fire to it from a safe distance, thanks to which you can clear the whole corridor of enemies. Don't try to get through the corridor beforehand - while fighting the Skeevers you might accidentally touch the wall with your weapon, creating a dangerous spark (in which case you will burn together with the enemies).
After crossing the dangerous part of the tunnel, keep going along it. You should quite fast come across a locked gate on the right - picking the lock will let you access a small cell (screen above). Inside it you will find the Guide To Better Thieving (+1 to pickpocket) and a chest containing a minor healing potion and some gold.
After taking everything you think might come in handy, return to the main part of the corridor. Keep following it, until you reach a bigger room. There kill two Skeevers and avoid a trap beside the exit (screen above). Afterwards go up the ladder to the surface\.
New main objective: Clear out Aringoth's safe
After getting out of the sewer, head to the Goldenglow Estate - the big building right beside you. Lockpick the door and head inside. Remember to sneak all the time - you aren't welcomed here and the guards will raise an alarm if only they get your trail. You don't however need to stay discreet at all costs - killing all the enemies won't affect the mission outcome in any way.
After entering the building, you should see an information that you need to obtain the key to Aringoth's safe. It's not necessary to complete the mission itself (you can also pick the safe lock), but creates an interesting alternative.
Thieves Guild quest unlocked: (Optional) Obtain the key to Aringoth's safe
Sneak through consecutive rooms, avoiding getting noticed by the guards - two of them are sitting by the table and one is patrolling the corridor. Tricking them is trivial - you just need to avoid the one who's patrolling the area (screen above) and will be able to freely explore the building afterwards. If you don't want to look for the key to Aringoth's safe and head to the safe at once, you will need to head to the basement. Therefore open the steel door to the basement and go down the ladder (screen below).
After reaching the lower level, open the door leading to the Goldenglow Estate Basement. In the corner of the room you will find two enemies who you can ignore completely - they won't notice you if only you sneak past them quietly. The enemy in the next room might prove a bit more problematic - he's sitting in such a position that he will spot you if you want to reach Aringoth's safe. You might play cat and mouse inside the corridor with him, therefore gaining access to the lower level of the basement (a bow might come in handy to create noise in distant parts of the corridors). A much better tactic is however setting fire to the substance on the floor- the enemy is sitting in the middle of a big puddle, so he'll burn (screen below). Once he's dead, just take his basement key - it will let you move throughout the building easier.
After dealing with the human torch, you can head down to reach Aringoth's safe (screen below). If you have obtained the key (see Obtain the key to Aringoth's safe), opening it won't be a problem. Otherwise, you will have to use picklocks, though the end result will be the same. After opening the safe, take the Goldenglow Bill of Sale - it's a very important document, in which Brynjolf will be very interested.
Leave the building afterwards - you can either do it by following the same way you came here, or through the sewers (passage to right of the safe).
New optional objective: Obtain the key to Aringoth's safe
After entering the Goldenglow Estate, try to reach the second floor. It's not all that difficult - two guards are be sitting by the table with their back to you and one is patrolling the corridor. He can be easily avoided by going through the parallel room. Afterwards go up the stairs onto the upper level.
You shouldn't have any trouble here as well - only three guards who can be easily tricked by going through the rooms that are out of their sight. Keeping everyone alive isn't required during this quest, so you can kill all the guards if you only wish to.
After reaching the room in which the key is, you will be in for a surprise - as it turns out, the key is in the pocket of Aringhoth himself. There are a couple ways of solving this problem: you can sneak to him from behind and steal the key, persuade him to give it to you out of his own free will (Speech) or take it by force. In the latter case, you will unfortunately have to take into account that all his servants from this floor will come to help, so it's not the optimal solution.
Regardless of which solution you choose, while inside Aringoth's room you should steal the Queen Bee Statue from the table - Delvin Mallory will buy it from you with pleasure.
New main objective: Burn three bee hives
After taking care of Aringoth's safe, you will still have to deal with the hives at Goldenglow Estate. The order here is very important - if you start by setting the hives on fire, quietly infiltrating the basement will be made much harder.
The hives can be set on fire in a few ways - with a bow enchanted with fire, spells or with a torch. Regardless of the method, you should quickly approach the hives and set them on fire. There's no sense in sneaking, as the hives are protected so well that reaching them unnoticed is pretty much impossible. Therefore the best solution is sprinting towards them and setting fire to all three (look out not to destroy any more - Brynjolf won't be happy and will cut your payment).
After the fire gets above the palisade, jump into the water and run from the Goldenglow Estate. You should head back to The Ragged Flagon, where Brynjolf is.
New main objective: Return to Brynjolf
After getting out of Goldenglow Estate, go meet with Brynjolf and give him the documents that you found in Aringoth's safe. The red-haired thief will pay you for completing the mission (100 gold) and let you use the Guild equipment - from now on, anything you find at The Ragged Flagon you can keep for yourself. Use the chance and check all the chests and barrels that you come across.
After satisfying your greed, you can move to the next mission. Brynjolf suggests that you should meet with Maven Black-Briar.
Thieves Guild quest unlocked: Dampened Spirits