If you haven't yet but would like to have a shot at the closed beta, you can do so either by logging into your Battle.net account and heading to the Beta Profile page, where you can elect to opt-in. After that you'll have to wait for an invite, which will be delivered via email. If you do receive an invite, it will also appear on your Battle.net account, so you can check there too. Anyone in the comments gotten one yet? Just curious!
Oh, and in case you're wondering, there is no NDA for this closed beta. None, nada, zip. Film your matches and broadcast them to the world, take screenshots, write detailed blog posts, go nuts. Just remember to report bugs so the Hearthstone team can get on them. Good luck to those of you who are hoping for an invite, let us know how it goes!