In most Blizzard games a user can press Print Screen on their keyboard to take an in-game screenshot. Unfortunately, when I try to do this in Hearthstone I am getting a screenshot of my Windows 8 desktop. How do I take an in-game screenshot of Heathstone?
Hearthstone unfortunately does not have a native screenshot function like in other Blizzard games at this time. For now you will need to take a screenshot using a program like FRAPS if you're unable to get a screenshot using Print Screen.
Apparently it is normal for this particular feature to be omitted and added much later in Blizzard's development cycles, so you should probably expect it Soon™.
The Hearthstone Closed Beta Patch Notes - 220.127.116.1117 indicate that "the PrintScreen key now takes a screenshot of your game and saves it to your desktop."
I use the Windows Snipping Tool. Simple, yet effective. Provided you're not trying to take a screenshot of anything that is going to disappear from the screen shortly.
EDIT: I should mention that I run the game in Windowed mode and then maximise the game using Task Manager to get it into position correctly.