How do I obtain the Nightingale Armor?

I have seen this armor in Skyrim around the internet, and I have no idea how to get it. I think it may have something to do with Thieves Guild, but I don't know any more. How do I get this armor?

From the Skyrim wiki:

Acquisition

The full set is given to the Dragonborn by Karliah before performing the initiation ritual of the Nightingales during the quest "Trinity Restored" for the Thieves Guild. All pieces are obtained when activating the Armor Stone, emblazoned with the Nightingales symbol, inside Nightingale Hall.

You are correct in that you will need to join the Thieves Guild. After running through the Guild's main questline, you will reach the quest Trinity Restored, in which your character is invited to join the Nightingales. The armour will be provided free as part of the initiation ceremony.