Dawnguard is out for Skyrim on the Xbox 360, and you can pick it up right away from the Xbox Live Marketplace.
and the quickest and fastest way to get to the new content is to listen to the guards (you know, the same ones who talk about being adventurers, taking arrows to the knee, and making fun of you for losing your sweetroll) as they gossip about new rumors.
If you happen to be out in the wilderness away from the guards, a courier will approach you to deliver a letter relating to the Dawnguard.
You'll only hear the new gossip or receive the letter if your character is above level 10, for the content in the Dawnguard expansion is tailored for experienced characters rather than newbies.
If you're below level 10, you can head to the Dawnguard keep southeast of Riften to initiate the quest line—but we really recommend against it. The difficulty of the new content is comparable to the expansion packs for Bethesda's previous game, Fallout 3.
Once you've reached Dawnguard, you'll be presented with an option along the way to side with either the vampire hunters (the titular Dawnguard) or their foes, the Vampire Lords. I won't say much more than that, except that if you intend on acquiring vampiric powers, you should side with the bad guys.
You can pick up Dawnguard from Xbox Live Marketplace for 1600MSP. It weighs in at half a gig (or 581.70mb) so be sure to free up some hard drive space. The PlayStation 3 and PC versions are forthcoming, but have not been officially announced.