Once you have the four city influences quests done (the ones in Markarth, Whiterun, Windhelm, and Solitude) you will automatically receive this quest. Your objective is to speak to Brynjolf about becoming the new Guild Master. We can certainly manage THAT, no!? Go talk to Brynjolf, who will be in the cistern along with EVERYONE else (everyone and THEN some). Follow him out to the middle of the cistern and a short and sweet ceremony will take place where everyone will proclaim you the new Guild Master.
After the ceremony, talk to Brynjolf again. He will give you two items: the AMULET OF ARTICULATION (which will make almost ANY Persuade speech check succeed and makes your speechcraft 30% better) and the GUILD MASTER TRIBUTE KEY (which unlocks a chest by the Guild Master desk that will be periodically refilled with your CUT of the guild profits). He will also tell you to go see Tonilla about obtaining your Guild Master armor.
Go see Tonilla and you’ll get a COMPLETE SET of Guild Master armor, which is FAR superior to your old Thieves Guild armor. Well, congratulations thief, you have done well for yourself. Lead your guild to success!