The Heroes of the Storm Technical Alpha is live! You can watch streams of the game over here!
Also, Blizzard has posted an article helping players install and access the game.
We’ve invited a limited amount of US-based players, including testers opted-in via Battle.net, friends and family members of Blizzard employees, as well as a number of international press sites and community contributors, to participate in this very early Technical Alpha testing phase. If you haven’t received an invitation to the Tech Alpha yet, make sure you’ve elected to participate in Heroes of the Storm testing by opting in on your Battle.net account’s Beta Profile Settings page. By doing so, you’ll give yourself the best chance at gaining testing access as our needs evolve and we expand the pool of invited players in the weeks and months to come.
You can check out this article here.
Twitch.tv - Heroes of the Storm
Battle.net - The Heroes of the Storm Technical Alpha is Now Live!