Turn each chair upside-down.
Unscrew the bolts holding the seats in place. Set aside the bolts. Lift the seats out of the chair frames.
Pull out the staples that hold the seats' old fabric in place, using a flat-head screwdriver and pliers. Discard -- or clean and repurpose -- the old fabric.
Inspect the seats’ foam and any cotton batting overlaying the foam for mold, a musty smell, decompression or flattening from wear, or dust, which indicates foam breakdown. Replace foam and padding that shows any sign of these problems with new 1-inch thick foam and new cotton batting.
Use the plywood seat as a template for new foam, if you are replacing it. Cut each piece of foam around the plywood, using a utility knife. Spray the plywood seat tops with spray adhesive. Position a foam square evenly on each plywood seat.
Use the plywood seat as a template to cut new cotton batting for each seat, if you are replacing the overlay material. Cut generously around the seat with about 4 inches to spare, using scissors. Center one seat, foam-side-down, on a cotton-batting square. Pull one edge of the cotton onto the plywood. Staple the cotton to the wood. Pull the opposite edge of the cotton onto the plywood. Staple it to the wood while keeping it taut. Continue to staple the cotton square’s two remaining edges to the plywood in the same manner. Staple the square’s four corners to the plywood, folding the material as if wrapping a gift, while holding it tight. Staple the remaining batting squares to the seats.
Cut a generous vinyl square to cover each seat, using the seat as a template. As with the cotton batting, cut the vinyl a few inches longer on each side than the seat. Center a seat -- foam-side-down -- evenly over a square of right-side-down vinyl. Staple the squares to the plywood in the same fashion as you attached the cotton batting.
Bolt the seats back on the chairs.