I pre-ordered from Amazon for PS3. The game was delivered on Sept 18th, and about 1:30 that afternoon, I got an email with the code for Borderlands Premier Club. Signed into Playstation Store and selected Redeem Codes. The download was pretty small. After download was complete I started the game.
The Golden Key - I get a message that I have the golden key (I don't see it in inventory) but I haven't used it yet in Sanctuary - I haven't found where to use it and haven't really looked, since the higher your level the better the prize, so I'm waiting.
Vault Hunter's Relic - The first character created (and each subsequent character created) has a Vault Hunter Relic in their inventory. To see it, hit the Select button (or the equivalent on your platform) to view your inventory. On the left side where your equipped items are, scroll down past the weapons to where there are 4 slots in a grid. The 4 slots are for your Shield, Class Mod, Grenad Mod, and Vault Hunter Relic. It provides a boos to Rare Find.
Gearbox Gunpack - In Borderlands 1, each character started with a single weapon specific to their character class. In BL2, each character starts with 4 weapons, two equipped and two in inventory. That is your package of guns to get you started.
The Mechromancer class - not yet released, but you should have a message indicating that you are a premier club member and will get the Mechromancer when it is released (shows up in game lobby, lower left on the screen).
Update: I actually had used the Golden Key without realizing it. In Sanctuary, near the fast Travel station, there is a golden weapons crate. Use the Golden Key to open that. When I opened it as a level 9 Assassin, I got two purple weapons - a sniper rifle and an SMG. The sniper rifle is awesome (fast fire rate, large magazine, fire damage, good scope) and is my primary weapon, so it was worth it.