Write or choose a story for your play. It needs to be one that will work well with the limitations of the medium, which are that you are communicating only with shapes, words and possibly music.
Create or purchase the puppets you need. These are essentially cutout paper dolls, sometimes with articulated arms.
Run a totally opaque screen across the stage to a height of about 4 feet. Your puppet operators will be behind this as they operate the puppets above them.
Place a partly transparent screen above the other one, overlapping it slightly. Cotton works well for this.
Put a series of lights about 4 feet off the ground and turn them on. Turn down the other lights in the theater. When you puppets move behind the transparent screen, the audience will be able to see them.