Hearthsteed looks like a magical Pegasus, with a nifty blue glowing effect. Dataminers had previously found a red glowing version of the mount in a WoW patch, which was presumed to be the Horde version of Hearthsteed, although this is not the case at present--you'll only get a glowing blue version right now.
To obtain the mount, you'll need to win three games against real, human opponents in Hearthstone's Play or Arena modes. Not too tricky… but it does mean you'll have to play enough Hearthstone to get a basic understanding of the game.
If you've been playing Hearthstone already, you'll need to get three more wins to be eligible. You'll know you've got it when you see the Mount Up! award (pictured right).
Obtaining Hearthsteed will also give any of your World of Warcraft characters the "Hearthstoned" achievement.
Blizzard also recently announced that players will be able to upgrade one World of Warcraft character to level 90 by preordering upcoming expansion World of Warcraft: Warlords of Draenor.