This is one of the 4 factions in Skyrim, best visited early by stealth-centered characters, since there are various trainers to your liking to be found. In order to find and join them, you will have to go to Riften, which can be reached by using any of the coaches outside any Hold's stables. (Whiterun should be the first you'll encounter.)
Upon entering the city, you'll be greeted by a shady character, asking what business you have in town. The outcome doesn't matter, he'll either direct you to Brynjolf, or Brynjolf will approach you himself.
Do his quest - you can fail the quest without consequences - and he'll invite you to the lower parts of town, namely 'The Ragged Flagon'. Get there in one piece and you'll receive an additional quest which involves beating up a few shopkeepers. Complete it and you'll be rewarded with a spot in the guild and this achievement.