In short, you'll need to install the Battle.net App first, then you'll be able to install Hearthstone from the Battle.net App.
You can also get to our downloads page by clicking EXPLORE at the top of the page, and then Game Client Downloads.
New to Hearthstone and having trouble obtaining cards? Our fantastic Blizzard Customer Service folks have created a new video to teach you how to obtain cards, how to navigate your collection and how to use Crafting Mode! You can watch it here!