Measure the height and width of the wall cutout. Measure at multiple points to ensure that the opening is an even rectangle.
Use a drywall or circular saw to cut away any material in the corners of the cutout if it is round or irregularly shaped. Measure the new opening's dimensions.
Cut a piece of drywall for an interior wall or plywood for an exterior wall that matches the size of the cutout. Insert the material into the cutout to ensure that it will fit.
Insert a piece of scrap lumber, such as a 1-by-3, into the cutout to act as a brace if the opening is more than a few inches high and wide. Screw the lumber into place at the top and bottom of the cutout with a handheld drill equipped with a screwdriver bit.
Mount the drywall or plywood sheet into the cutout and screw it into the brace. Apply joint compound with a putty knife to fill the gaps around the material. Sand the joint compound smooth with medium-grit sandpaper once it has dried.
Apply paint to the entire wall with a brush or roller. Add additional coats until the enclosed cutout blends in with the existing wall.