Cut the lumber into the lengths you'll need with the circular saw. Cut the 1-by-12 lumber into two pieces of 24 inches and two pieces of 21 inches. Cut the pegboard and plywood into 24-inch squares.
Stand the 1-by-12 lumber on edge and arrange the pieces into a square. Tape the edges of the square together with the duct tape. Drill through each corner of the square with the 1/8th-inch drill bit (a total of eight holes). Secure each corner with a 2-inch screw.
Place the pegboard over the open top of the square, aligning the edges. Drill through each corner of the pegboard into the wooden frame below. Secure the pegboard to the frame with screws.
Flip the box upside down, so the pegboard is on the bottom and the top is open. Place the linen cloth into the bottom of the box, covering the pegboard.
Cut the insulation with the box cutter into five pieces of 12-by-21 inches. Lay the insulation on its edge into the box on top of the cloth. The insulation should completely fill the box, but should not be compressed.
Place the plywood over the open top of the square, aligning the edges. Drill through each corner of the plywood into the wooden frame. Secure the plywood to the frame with screws.