Stand two side chipboard pieces parallel to each other on their smallest ends. Set the top chipboard piece on top of the side pieces. Move the side pieces outward until the outside edge of each side piece is flush with the ends of the top board. Predrill four holes through the top chipboard piece and into each side piece, so that the holes are directly in the center of the side piece and evenly spaced. Fasten the pieces together with 1 1/2-inch chipboard screws. Rotate the cabinet upside down, and attach the bottom piece by following the same method.
Set the assembled chipboard cabinet on its face on the working surface. Lay the rear piece in place on the back of the cabinet, and adjust the edges so that the edge of the rear piece is flush with the outside edges of the cabinet pieces. Predrill into the rear piece and down through the end of each adjoining board, placing holes every 8 inches around the perimeter. Fasten the pieces together with 1 1/2-inch chipboard screws.
Position a shelf board inside the chipboard cabinet, and set the shelf at the height desired. Mark each side piece with the shelf's height, and then mark the rest of the shelf locations. Drill two holes in each side piece at the level of each marking, being careful not to break through the outer surface of the side pieces and using a drill bit with exactly the same diameter as the pegs to be used. Slide a peg into each hole. Set the shelves on top of the pegs.
Rotate the assembled cabinet so that its back is touching the working surface, and set the door piece in place. Position two hinges evenly so that the entire door is supported, and mark the location of the hinge screw holes in the side piece and the door piece. Predrill a 1/2-inch deep hole at each marking, and fasten the hinges to the side piece and the door piece with chipboard screws. Test the door to ensure smooth operation.