How do I begin playing DLC?
You start the DLC by using the Fast Travel system to go to the first area of the DLC. From there, you'll receive a new mission and further instructions. These are the areas you're looking for:
- Captain Scarlett and Her Pirate's Booty: Oasis
- Mr. Torgue's Campaign of Carnage: Badass Crater of Badassitude
- Sir Hammerlock's Big Game Hunt: Hunter's Grotto
- Tina's Assault on Dragon Keep: Unassuming Docks
Note that you may be restricted from playing DLC by your level and/or story progression.
I thought DLC in the first game was handled by opening new fast-travel locations - you received the quest when travelling to them. I would assume it is the same for Borderlands 2.