Examine the frame of the stool. Push against the legs and joints to see if there are any loose areas. Loose joints should be repaired with glue; if the legs are coming away from the support struts, then replace any missing nails using the existing nail holes.
Turn the stool upside-down and check the bottom of the seat for nail heads holding the seat cover in place. Remove any nails if you can with the claw end of a hammer. If the upholstery has been glued into place rather than nailed, cut it away carefully with a craft knife, trying not to damage the seat of the stool.
Remove the padded seat of the stool to use as a template. Lay it on top of the new foam and draw round it with a marker pen. Cut the shape out with a craft knife.
Lay the batting out and place the new foam seat on top. Fold the batting over the foam so that it completely covers the sides and cut off any excess from the center. Lay the fabric out right side down and lay the foam seat on top. Fold the fabric over to make sure you have sufficient allowance to cover the sides and then cut off any excess.
Rub the frame of the stool with medium-grade sandpaper, working with the grain of the wood. Pay particular attention to any knocks or chips and sand away the edges of the damage to make it less visible. Remove any traces of the old finish.
Paint on a coat of undercoat, brushing in the direction of the grain of the wood, and leave it to dry completely. "Key" it lightly with fine-grade sandpaper to provide a good surface for the top coat. Apply the top coat of paint and leave it to dry completely.
Glue the new foam seat to the top of the stool. Lay the fabric on the ground, right side down, with the batting on top. Turn the stool upside-down onto the batting. Fold the batting and fabric around the sides of the seat as tightly as you can and fasten them to the underside of the seat with upholstery nails.