Barbarians Beware: Diablo III Closed Beta Begins
Note, that won't mean everyone will get a beta key. Some will, but many will not. In addition, Blizzard will be providing keys through beta promotions and giveaways.
The closed public beta is so new, there aren't even any beta keys being auctioned on eBay ... yet. Truthfully, we fully expect there to be beta key auctions, soon.
And there may be plenty of takers. Based on what Blizzard says on its site, if you haven't received a beta key in your email (beware of phishesrs) or if you've checked your Battle.net account and don't see the D3 beta there, you'd better hope for a chance via a promotion or giveaway.
As far as "when" the game will release, it's been available for pre-order on sites such as Amazon.com since mid-2010. There's still no indication from Blizzard as to when the game will release, and Amazon.com still has no date available, either.