The Heroes of the Storm technical alpha is now active. If you're lucky enough to get in during the first wave, it will appear in the Battle.net launcher for you. You'll be able to download the game and then play. There also was a short private email from Blizzard announcing the alpha -- note that it was not flashy as most emails are from Blizzard. We're giving these details so you don't fall prey to any phishing attempts.
If you wish to sign up for your chance to enter the beta, you can do so via the Heroes of the Storm website or your Battle.net account page.
Known live streams of the alpha tonight:
Gallery: Heroes of the Storm: Overview