On the PTR, it was really easy to get attuned to the big new tier 6 raid, the Black Temple. All you had to do was be at least Honored with the Violet Eye and talk to Johnny McWeaksauce, and you'd get the amulet that served as a key. So it actually never occurred to me to wonder what the attunement process would be like in the live patch.
In case you were wondering, however, wonder no more. MMO-Champion has all the details (plus screenshots), courtesy of Arthyn from Vanquish (A-Staghelm). In short, you have to kill Fathom-Lord Karathress (a boss in Serpentshrine Cavern) and Al'ar (a boss in the Eye). The detailed version is after the cut, for reasons of length and spoileriness.
Update: apparently, Karathress and Al'ar are just the first parts of the attunement chain. After Al'ar, you have to kill Rage Winterchill, the first Hyjal boss, and even that may not be the end -- we'll just have to see. World of Raids has screenshots of the new quests.