Sign up for Hearthstone beta!
You can sign-up for Hearthstone beta from battle.net (you will be redirected depending on your region). The game has a tab there for Hearthstone, on the landing battle.net page.
Login into your battle.net account, click on the Hearthstone tab, you will be redirected to http://eu.battle.net/hearthstone/en/, click on “Beta sign-up” and enable “Hearthstone” from the next page. Hit “Update preferences” to save.
A date when the beta participants (for Europe) will be able to play the game wasn’t announced yet but this is what is noted in the FAQ page:
“I don’t live in the US; can I still participate in the beta test?
We hope to launch a beta test in other game regions after the initial beta-test launch in North America, but we don’t have any specifics to announce at this time. Stay tuned for updates.”
The beta test is not available outside US at this time, even if you try to login to us.battle.net instead of eu.battle.net, you will see the same thing. Just an option to opt-in for beta.