There is a button that says Menu on the bottom left of your screen. Then click on the Bitizens icon (which is the first one). Next, you pick any bitizen that is living in your tower and choose dress-up. A large green button with the word costumes should be there.
You can't "buy" any costumes in Tiny Tower. You have to either randomly deliver a person wearing costume in the elevator, or the tasks the game gives you sometimes ask you to take people wearing a certain costume to a floor in the elevator