Those who pre-ordered Borderlands 2 are eligible to receive a number of pre-order bonuses including new character class called the Mechromancer (which is slated for release in the near future, as of this article), a Vault Hunter’s Relic, a Golden Key, and a Gearbox Gold Gun Pack.
With exception to the Mechromancer class, players are supposed to receive each of these items after creating a character and speaking to the Claptrap robot at the start of the game.
That being said, many players have been unable to receive any of these items, because the pre-order bonuses appear to be bugged. For whatever reason, the DLC menu in game shows that the Borderlands 2 Premier Club content is ‘purchased’ but ‘not downloaded’.
There are ways to acquire additional Golden Keys and some bonus items. I've detailed some methods here.
As of this posting, neither Gearbox nor Steam appear to have acknowledged the problem, but due to the fact that the problem appears to be widespread, we expect a fix to appear shortly. We've reached out to Gearbox for a statement.
Update: I've been informed by readers that restarting steam and verifying the game cache of Borderlands 2 will allow you to download five previously unavailable files and enable the Premier Club pre-order bonus content.