Adjust the miter saw to cut at a 45-degree angle and lock the saw in place. Place one 1-by-18-by-18-inch board flat on the miter saw table and cut the ends at a 45-degree angle on the same 18-by-18-inch side of the boards. Repeat this process for each board.
Sand the board ends’ cut edges with a fine-grit sanding block until they are smooth. Sand with the wood’s grain.
Place the four boards together for a square assembly. The mitered board ends should fit together like a picture frame. You should have an 18-by-18-inch square assembly.
Drive trim head screws through each corner joint every 2 inches using a screw gun to fasten the square assembly together.
Lay the 1/4-by-18-by-18-inch plywood panel over one open side of the assembly. Align the edges of the plywood with the outside edges of the assembly. Hammer finish nails through the plywood into the edges of the assembly every 2 inches around the entire perimeter of the panel to secure it in place.
Brush two even coats of wood finish onto the box shelf assembly with a paintbrush. Allow the finish to dry for four hours between coats. Wait 24 hours after the final coat before using the box shelf.