Pompeii had two theaters, where plays were produced, and an Amphitheater for open-air shows such as gladiatorial combats (see Stage 8 of the Cambridge Course).
The larger theater was typical of the Greek and Roman theaters of the time : a semi-circular arrangement of tiers of stone benches, facing a rectangular stage. There were entrances at the sides and center back of the stage for the actors and chorus to make exits and entrances. No scenery was used - an actor would announce to the audience where the scene was set.
The smaller theater, called the Odeon, was built similarly, but had a roof. See p. 216 of the Cambridge Course for a photo of the model of Pompeii, showing the two theaters.