Measure, mark, and cut the mat and the backing board to fit your frame. Mat board is available at art supply stores; plywood or heavy cardboard can serve as backing. If the art is valuable, use acid-free matboard and backing.
Place the art on the right side of the mat to determine the size of the opening through which it will be seen or, if the art has a border, measure the area you want to show. Locate the opening so that the side borders of the mat are equal, and the bottom border about 1/2 inch wider than the top.
Mark the opening a fraction of an inch smaller than the art so that the mat will overlap the edges of the picture. Use a steel ruler or a framing square and either a mat cutter (sold at art supply stores) or a utility knife to cutout the opening. Bevel the edges of the cut inward so that the mat’s thickness will show from the front. After cutting all four sides, use a singleedge razor blade to clean the corners of any fuzz or uncut scrap. Smooth rough spots with an emery board.
Fasten the top of the art to the backing board with tape hinges. Then tape the mat to the backing board.