What to wear: Unless you're already 20 feet tall, just forgo the height aspect of this costume and focus on finding the thickest, burliest, furriest coat and pants to wear. Wun Wun, a Wildling giant, wrapped his boots in string and cloth, and had a few animal bones hanging from his belt. Not to be a downer, but you could also have a few arrows sticking out of your costume in various places to drive it home. Make sure you wear a long dark wig and add in some facial hair, too.
How to act: Wun Wun wasn't the most eloquent of characters, so keep whatever you're saying short and simple.