Measure the length, height and depth of your microwave. Cut a piece of 3/4-inch plywood to 1 1/2 inches more than the length and depth, and one piece to 1 1/2 inches more than the length and height. For example, if your microwave is 16 inches long, 14 inches deep and 12 inches high, cut a piece 17 1/2 by 15 1/2 inches for the bottom of the wall support, and a piece 17 1/2 by 13 1/2 inches for the back of the wall support.
Lay the bottom piece of plywood flat on a work surface. Stand the back piece of plywood up along the back edge of the bottom piece, so that a right angle is formed. Glue the back piece onto the bottom piece of plywood and let dry.
Turn the bottom piece of plywood over and drill a pilot hole every 3 to 4 inches along the joint of the bottom and back pieces, then secure with 1 1/2-inch screws.
Turn the shelf back over so that it is sitting on the bottom. Fit an L-bracket into the corner formed by the back and bottom pieces, flush with the outside edges of the plywood. Secure the bottom portion of the brackets in place with 1/2-inch screws through the bracket screw holes into the bottom of the shelf.
Paint the shelf and brackets and leave to dry before installing the shelf.
Position the shelf against the wall and use a level to ensure the shelf is straight. If you don't have a masonry wall, then use a stud finder to locate wall studs to attach the shelf to.
Secure the shelf to the wall with 3-inch screws through the back portion of the L-brackets as well as through the corners of the back panel of the shelf. Touch up the screw holes with paint and let dry before placing the microwave onto the shelf.