First, plan your stage layout. This will depend on the number of sets your play requires, the amount of space on the stage and the budget for the production. Most flats are eight feet tall, and vary in width from four to more than 16 feet long. Remember that larger flats will cost more to construct and require a larger crew to move around on stage.
Most flats are built on a wooden frame that is light enough to move around on the stage but strong enough to support the weight of the flat. Pine 1x3 lumber works well for building a frame. It is soft and easy to cut, but strong enough for most types of flats, including heavier hard flats.
Turning the lumber into a sturdy frame is the next job. To build a frame from pine 1x3s, use dado joints to attach horizontal rails to vertical stiles. Space the stiles far enough apart to leave room for any windows or doors the flat will need. At the base of the flat, use a single long rail so that only one piece of wood actually contacts the stage surface. This will make moving the flat around much easier. Finally, add corner gussets or lumber reinforcements to the joints of the flat for added strength.
There are two types of theatrical flats. They differ in terms of what material they use for a skin over the wood frame. Soft flats use a pliable material like muslin or canvas. To build a soft flat, use dope (a 50-50 mixture of white glue and water) to coat the surface of the frame, then unroll the skin material over the flat and let the dope dry. Hard flats use a rigid material, like plywood or Luan, for a surface. You can attach this to the frame with nails or brads.
Choose a skin for your flat based on the decoration style. For example, if your flat is going to be painted, canvas may be best. If wallpaper is the final surface, a rigid Luan skin is a better idea.