Measure the depth, width and height of the washer using a tape measure. Add 4 inches to the depth measurement, then 2 inches to the height and width measurements to find an appropriate size for the washer cabinet. Repeat the process with the dryer to find the size of the dryer cabinet.
Cut two piece of three-quarter-inch hardwood to the height and depth of the washer with the circular saw. Cut one piece of three-quarter-inch hardwood to the height and width of the washer. Cut one piece of three-quarter-inch hardwood to the depth and width of the washer. Repeat this process for the dryer cabinet.
Cut two pieces of three-quarter-inch hardwood 2 inches wide and as long as the width of the washer. Cut two pieces of three-quarter-inch hardwood 6 inches wide and as long as the width of the washer. Apply wood glue to the ends of the 2-inch pieces. Attach one 2-inch piece to one edge of a washer height and depth piece, at the bottom of the height edge. Repeat for the dryer cabinet.
Glue and attach the 6-inch pieces to the opposite height-length edge of the cabinet piece. Attach the other washer height and depth piece to the other end of the 2- and 6-inch-wide pieces, to form a basic cabinet frame. Glue the top of the cabinet frame. Place the washer depth and width piece on top of the frame. Repeat to build the dryer cabinet.
Reinforce the joints on both cabinets with countersunk 1-inch screws and a hammer drill with a screwdriver drill bit. Screw two hinges onto one cabinet height edge of both the remaining washer piece and the remaining dryer piece. Turn the pieces over. Screw cabinet door handles to the edges of the pieces that are opposite the hinges. Stand the pieces up by their respective cabinets. Screw the hinges to the inside of the cabinet frames.