You can send your friends gifts via the special Gift Shop once you have verified your e-mail address in the game. You can do that by clicking on your friend's box in the friendship menu, and selecting the little icon with the box:
You'll be taken to a shop where you can buy gifts for your friends. More gift options will be added in the future.
Additionally, you'll sometimes have the chance to send friends a free gift from a selection of cards when you level up.