Remove the cushions and pillows from your couch. Turn it over so that the bottom is facing up. The bottom of the couch should face you at an upward angle.
Cut away any netting or fabric covering the bottom side of the couch with a shop knife and discard. Fit the foam inside of the couch's cavity, tucking into corners. Do your best to keep the foam flat and, if necessary, cut the foam to fit using the shop knife.
Align the top corner of plywood to the top left corner of your couch's underside. Fasten the plywood to the corner using a hammer and nail. Straighten the plywood so it is even against the edge of the couch, then drive another nail through the plywood and into the couch frame. Keep two to three inches between your first and second nail. Insert a nail every two to three inches along the perimeter of the plywood until you wind your way back to the first nail.
Sand the edges of the plywood to smooth the wood and flip the couch back over. If desired, stain the plywood to match the color of your couch's frame.