Blizzard has opened the floodgates for StarCraft II beta sign-ups. Interested folks should head on over to Battle.net and run the required system specifications check pronto.
Note that doing so does not guarantee beta access, but does automatically add your profile into a pool of considered applicants, which Blizzard will randomly select from for program inclusion. Those selected will receive an email from Blizzard with instructions for downloading the beta client and obtain a beta key. An exact rollout date for the beta has yet to be announced, so when those notifications might go out is anyone's guess. At any rate, it's best keep an eye on that mailbox.
Good luck!