Measure the portion of your air conditioner that sticks out through a wall opening or window with a tape measure. Note the rough depth, height and width at the unit's largest points on both sides, top, bottom and the back.
Add 3 inches to each of your air conditioner dimensions to produce the dimensions for the soundproof box. This will allow for a margin of error, as well as the thickness of the soundproof material.
Lay a 1/4-inch plywood sheet across two sawhorses. Mark the dimensions for the back of your box on the wood with a pencil and steel yardstick to act as a straight edge. For example, if your air conditioner is 24 inches wide and 18 inches tall, the back of your box will be 27 inches by 21 inches with the 3-inch clearance added.
Cut out the back of the box with a circular saw. Measure and mark plywood for the top and bottom of the box, as well as the two sides, and cut them following the same procedure.
Locate the air conditioner's rear vent, which serves to exhaust hot air. Determine where the vent will fall within your box and cut away part of one of the box sides with a circular saw to create an opening that aligns with the vent.
Cut acoustical foam panels or sheets with a utility knife into five pieces that are slightly smaller than each piece of plywood.
Apply liquid or spray-on foam adhesive to the center of each plywood box piece. Place a smaller amount of adhesive about an inch inside the edges of the plywood and press the corresponding piece of acoustical foam into place firmly. Hold for several seconds before releasing and gluing the next panel.
Assemble the five sides of the box by screwing 2-inch wood screws through the plywood, spaced several inches apart. Attach all five sides of the box so that the acoustical foam faces the box interior. Position the opening for the air conditioner's vent at the appropriate location.