There are two main types of flats, Broadway or canvas, and Hollywood or wood. Canvas are the most common in schools because they cost less to build and are light weight and easy to store. Wood flats are used in television and at the college level because they are sturdy, easy to configure, and if built properly can last for decades.
Here are some videos showing how to make each type of flat.
For our stone wall project I had some old flats that needed new canvas, so that is what we will run with.