Lay out two maple melamine boards, 3/4-by-24-by-36 inches, parallel to one another on their long, thin sides. Have an assistant hold the boards in place, 24 inches apart. Set another maple melamine board, 3/4-by-24-by-24 inches, against the ends of the other boards, which are the side boards of the cabinet.
Set 1-inch metal L-brackets every 6 inches along the joint between the side boards and the other board, which is the top board. Mark each bracket screw hole on the top board and the side boards. Drill each hole and attach the brackets in place with 3/4-inch wood screws. Repeat to attach another identical board to the other side as the bottom board.
Set a melamine board, 3/4-by-24-by-37 1/2 inches, on the working surface and place the assembled frame on top of it. Set 1-inch metal L-brackets every 6 inches between the frame and this larger board, which is the rear board. Mark the screw holes for each bracket. Drill the holes and attach the brackets in place with 3/4-inch screws.
Flip the cabinet frame over and set another melamine board, 3/4-by-24-by-37 1/2 inches, on top of the frame. Position two side-mount cabinet hinges between this board, which is the door, and one of the side boards. Mark the locations of the hinge attachment holes, lifting the door if necessary. Drill each hole and attach the hinges in place with 3/4-inch wood screws.
Position a magnetic latch between the door and the other side board. Mark the attachment holes on the door and the side board and drill them. Attach both parts of the latch with 3/4-inch wood screws.