According to the Warcraft Facebook page, the World of Warcraft: Mists of Pandaria beta is going to be starting pretty soon. What's going to happen is, players will be invited in waves, based on how long they've had a WoW account, and also based on how early they got their Annual Pass. As you know everyone with a WoW Annual pass (that is a one year non-suspendable subscription) gets a free mount (Tyrael's Charger), Diablo 3 for free (coming out May 15th) and beta access to Mists of Pandaria.
So log-on to Battle.net and update your system specifications info and check the Warcraft Beta option to make sure you're not overlooked when the time comes to dish out beta codes. You'll need to download a small program that is going to evaluate your graphics card, processor, among other things. As with code giveaways I'm sure there will be plenty to go, but in the meantime your best bet for the Mists of Pandaria Beta, if you don't own an Annual Pass, is to upload your system specifications to Battle.net and hope that your rig is unique enough to warrant Blizzard's attention.
In the meantime the Non-Disclosure Agreement on the WoW: MoP media event fell so here's some more reading for those who are interested to know what to expect from the early stages of the Beta:
GameTrailers Scarlet Monastery and Scholomance Heroics, the new Zones and class, all stuff I'm going to cover, when I can get my hands on it, which should be within a week or two if we trust Blizzard to not keep us waiting for too long.