There are many common methods to arrange and operate scenery:
Wing and Drop - Wings, backdrops and teasers are painted to look like one scene, and then can be changed to another set for a scene change.
Gripping - Closing a downstage curtain to allow the carps to change scenery before revealing the scene again.
Flying - Scenery can be flown in and out using the counterweight fly system.
A Flat is a stiff flat piece of scenery that sits on the floor, using supports called jacks or stage braces.
A Jack is a triangular brace at a 90 degree angle to the floor.
A Stage Brace is a single piece with one end hooking to the top of the flat and the other end screwing down to the stage to support the back of the flat.
Flats can also be lashed with rope or cords in a zig-zag pattern across the seam.
A Box Set is a set that wraps around an area, creating a three sided room.
A Periaktoi is a triangular flat that can be rotated to display different scenes.