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Start by cutting four pieces of 1/4-inch maple veneered MDF to 24 by 12-inches to form the top, bottom and shelves. Cut two pieces of 3/4-inch maple veneered MDF to 28 by 12-inches for the sides.
Using a router or a table saw, cut a 1-inch rabbet groove into one long side of each piece.
Starting with the two side pieces, use a biscuit joiner to cut two grooves 3/8-inch from the top of the pieces. They should be 1/3 of the way in from both edges. Repeat this step 1/3 of the way down, 2/3 of the way down and once more 3/8-inch from the bottom of the pieces.
Lay the timber flat on a level table or workbench. Next, cut two biscuit grooves into the sides of the top piece, bottom piece and shelves. Cut grooves both 3/8-inch from the top and 1/3 of the way in from the edges. Make sure all the pieces are cut to the proper dimensions and are close at hand before starting the gluing process.
Apply glue inside the two top biscuit grooves on one side piece and the top piece. Insert a biscuit into the side piece and attach the top piece, making sure the rabbet grooves are both facing in and to the back. Place glue on top of the biscuits. Repeat the process to connect the two shelves and the bottom piece, again making sure the rabbet grooves are facing in and to the back.
Take the last side piece and fill all the biscuit grooves with glue, then insert a biscuit into the grooves. Place glue on top of the biscuits.
Fill the remaining empty biscuit grooves on the top, bottom and shelves with glue. Attach the last side piece, again making sure the rabbet groove is facing in and to the back.
Secure clamps to hold the piece together and let it dry. Wipe off any excess glue with a damp towel.
After the piece is dry, insert the backing into the rabbet grooves so it fits securely, leaving 3/4-inch at the back to hang the shelf.
Cut the piece of maple for the backing to 27 by 23-inches. Slide it into place inside the rabbet groove, tapping it into place with a mallet if necessary. Use a stapler to secure the backing into place, along the outsides edges and the areas that meet the shelves on the other side.
Staple 1/4-inch cutoff strips of maple around the perimeter of the backing to ensure the cabinet is secure and square. The strips also provide added stability when the cabinets are attached to the wall, giving the countersink screw something to grab onto.
For the trim, start by cutting down pieces of the 1/2 by 1-inch walnut to 28-inch long for the side pieces. Cut four pieces of the 1/2 by 1-inch walnut to 24-inches long for the top, bottom and shelf pieces.
Miter the edges to a 22.5-degree angle on the top, bottom and side pieces so they fit together nicely. Leave the two shelf pieces with a flat edge.