Lay down two 1/2-by-12-by-37-inch plywood boards on their long thin sides. Arrange them parallel to each other and about 2 feet apart to serve as the side boards of the box cabinet. Put a 1/2-by-12-by-25 1/2-inch plywood board against one end of the side boards, perpendicular to them, to be the top board.
Drill three holes through the top board and into each side board for a total of six holes. Set 2-inch wood screws in the holes and screw them down to attach the boards together. Repeat for the other end of the side boards to attach the bottom board.
Position another side board directly between the two other side boards, parallel to them and exactly in the middle. Drill two holes through the top and bottom boards and into the middle board. Attach the middle board to the cabinet with 2-inch wood screws.
Lay a 1/2-by-25 1/2-by-38 inch board over the frame and position its edges to make sure they are even with the frame. Drill holes every 12 inches through this board, which is the rear board of the cabinet, and into the frame boards, including the middle board. Set 2-inch wood screws in every hole and screw them down tightly.
Stand up the cabinet and hold a 1/2-by-12-by-12-inch board inside the cabinet at the desired shelf height. Mark the side boards and remove the shelf board. Drill two holes into each side board at that height and insert pegs in the holes. Set the shelf board on the pegs and repeat for three other shelves. Insert containers on each shelf.