For a simple postcard exchange just sign up for a free account on PostCrossing and for every postcard you send, one will be sent to you.
Try collecting one postcard from each of the 50 states or try collecting certain types of postcards. You can collect View Cards which are scene cards, landscape cards, cards with animals or Ad cards. [Ad cards are free postcards with advertisements on them]
What do you do with all the cards once you start swapping? I have a postcard wall where I keep all the cards I receive from friends. It gives me a visual of the world I communicate with. You could also just keep them in a scrap album or binder.