At 3:00 of this unboxing video for Battlefield 3 we're shown the card for Mass Effect 3's multiplayer beta, which says it will take place in January. Anyone who buys Battlefield 3 gets into the beta.
On its forums, BioWare just confirmed the Beta is "coming soon" and that there "will be multiple opportunities to qualify for early access." The surest is through the Online Pass included in new copies of Battlefield 3.
Notice of the exact date for the beta will be sent out over Battlefield 3's in-game ticker; you can also sign up for an email notice at masseffect3.com.
Battlefield 3 multiplayer gamers can also go ahead and access a set of N7 Mass Effect 3 dogtags.