If you have a Battle.net account with at least one attached Blizz title, you can opt in to the test via the beta profile page. After you do that, sit tight and wait for an acceptance email. If you have an annual World of Warcraft pass, you're automatically in, but Blizzard says that you might have a bit of a wait anyway due to its staggered invite waves.
Finally, there's no NDA for WoW's newest expansion, so you'll be seeing plenty more screenshots, video, and commentary flooding the web in short order. Check out our sister site for the latest and greatest MoP coverage.