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.
The January date was confirmed about 30 minutes ago on the Mass Effect Facebook page. Also, on its forums, BioWare said 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.
Kotaku will have hands-on impressions of Mass Effect 3's multiplayer for you next week.
[Thanks, Diebythesword, Paradox me and Corey S.!]