Place the 1-by-12-by-24-inch boards parallel to each other and oriented horizontally. The 1-by-24-inch edges should be resting flat on the work surface. Space the boards 22 1/2 inches apart from the inside edges. These are the top and bottom boards.
Place one 1-by-12-by-22 1/2-inch board between each end of the top and bottom boards to form a square box. These are the side boards.
Drive three evenly spaced pan head wood screws through the top and bottom boards into the ends of the sides with a screw gun.
Center the remaining 1-by-12-by-22 1/2-inch board between the sides. It should be parallel to the top and bottom boards. This is the center shelf board. Drive three evenly spaced pan head wood screws through the sides in to the ends of the center shelf board with a screw gun.
Lay the 24-by-24-inch plywood panel over the assembly. Align the edges so that they are flush with the outside edges of the assembly.
Hammer finish nails every two inches through the plywood panel into the edges of the sides, top and bottom boards of the assembly. This is the back of the bookshelf.
Brush two even coats of wood finish over the bookshelf assembly. Allow the finish to dry four hours between coats.