Dustin Browser announced a few minutes ago during the BlizzCon 2013 Opening Ceremonies that beta sign-ups are now active for the Heroes of the Storm beta.
If you're worried about how to find it, head to your Account page on Battle.net and then the Games and Codes menu. Under that, click Beta Profiles and you'll see the new Heroes of the Storm opt-in at the top.
UPDATE: The Heroes of the Storm cinematic has now been uploaded to YouTube in glorious HD. Thanks, Stiven!