The little booklet you get when you go to the theater is called a playbill. A playbill usually includes a list of the cast and production crew.
You can also call a playbill a program. At most theaters in the U.S., playbills are handed out to everyone in the audience as they enter. If you attend a Broadway play, you'll get a thick playbill with a lot of information about the play, the actors, and the venue—as well as a lot of advertising. A community theater or school production usually provides smaller, simpler playbills.