Hearthstone Battlegrounds was announced at Blizzcon a few days ago, and while the full version is yet to come, a playable beta is available now. If you want access to Blizzard's new auto-combat mode for Hearthstone, you've got quite a few options.
The first opportunity has already passed, but if you were a Blizzcon participant, you'll have access to the beta when it opens around 10am PST on November 5th. You will be able to keep this access until the end of the beta on November 12. If you bought a virtual ticket instead (or buy one now, as they're still available), you'll get access to the beta as well.
The third way to gain access is by first purchasing the Descent of Dragons Home expansion (either version).
However, for those who don't feel like being too fooled into beta access to a new game mode, don't worry - there's another way - you can link your Battle.net and Twitch.tv accounts.
It's a pretty straightforward process: go to the Twitch Settings menu (click your username at the top right and follow the drop-down menus), go to Connections under Settings, find the Battle.net section and follow the instructions. there, then click Connect, log into your Blizzard account and you're done. Finally, watch any feed under the Hearthstone category (not just Hearthstone Battlegrounds, any Hearthstone stream will do) and you'll have a chance to get free beta access.
This is tied to one event: the Battle of the Battlegrounds, where you can choose one of the four teams you need to root for. Anyone who pledges to that team counts towards that team's total wins, and the winning team, along with the people who pledged them, are awarded prizes. It should be fun to see who comes out on top.