While the release date of the second episode of Starcraft II isn’t due until March 2013, the beta access has been expanded not to only to the people that got invited, but for those who pre-ordered the game digitally.
Assuming you pre-ordered the game before December 18th, your account will be flagged to gain access to the Heart of the Swarm beta. You can download the client through Battle.Net and start playing through the game with bugs.
Pre-ordered the game after the 18th? Don’t worry, Blizzard will be doing waves in a weekly basis and then you can hope you get an access. Also, don’t forget that there are certain stores like Amazon that are giving beta keys.