In order to restore the Thieves' Guild to its former glory and assume the title of Guildmaster, you must perform 4 'special jobs' across four major Holds of Skyrim: Whiterun, Markarth, Windhelm, and Solitude.
In order to get a special job, you must first complete 5 smaller jobs in that hold. To get a job, talk to Delvin Mallory or Vex. The small job targets are randomized across the major holds and a tally of the small jobs is not visible to the player.
Jobs can be accepted and quit at will so if you have done all the jobs in a perticular hold select to quit the current job and ask for a new one (It can be the same style of job) untill you get the hold you need.
After completing 5 jobs in a particular Hold, Delvin Mallory will offer a Special Job in order to increase the Thieves' Guild influence in that Hold.
Once you have completed all four Special Jobs, it will start the 'Under New Management' quest. From here you can talk to Brynjolf to officially assume the title of Guildmaster but you will need to retrive you Thieves Guild armour so Do not sell it.
All of the above info and much more detailed information can be found at trueachievements.com