Here is how i installed it with Wine:
Download the Battle.Net Client
Install Wine(i believe both 1.7 and 1.6 work)
(Just go to ubuntu software center, and type wine)
Run "Wine Configuration" from your application menu
Go to the tab "Libraries"
In "New override for library", enter "dbghelp" and click "Add..."
Then in "Existing overrides", select "dbghelp" and click "Edit..."
In the window that just popped up, select "Disable" and click on "Add".
Back in "New override for library", enter "msvcp100" and click "Add...".
Do not edit this entry in "Existing overrides"!
Click on "OK"
Install and start Battle.Net and Hearthstone as you would on a Windows machine
Information found here:http://www.reddit.com/r/hearthstone/comments/23fwzq/tutorial_how_to_play_hearthstone_on_linux_via_wine/
Just note this:
You may or may not experiance minor glitches, since HS is not yet out for Linux.
Hope this helps.