Disassemble the chair. Remove screws, bolts or nails securing the parts of the chair, and gently tap any stuck pieces with a rubber mallet to loosen them. Pull out the staples holding the fabric to the upholstered pieces, and remove the old fabric.
Cover damaged areas of the wood with new wood putty. Smooth the putty on thinly and evenly with your fingers, and let it set completely. Reassemble the frame of the chair using finishing nails, but don't reattach the upholstered pieces.
Apply a thick layer of a gel finish stripper all over the wooden frame using a paintbrush. Let it sit for about 15 minutes until you see the finish begin to bubble and blister. Scrub the frame with the steel wool to remove all of the old finish.
Soak a rag with lacquer thinner, and rub it all over the frame to remove the finish stripper residue. Sand the whole frame with fine-grit sandpaper, and then wipe it clean with a tack cloth. A tack cloth is slightly sticky and will remove all of the sanding dust, unlike a regular rag.
Set aside the frame, and reupholster the remaining pieces. Use the old fabric and batting as templates to cut new upholstery, and follow the manner in which they were upholstered previously. Wrap the pieces with the batting and fabric, and staple these in place along the seams.
Apply the new stain to the frame of the chair, and let it dry for 24 hours. Cover the dried frame with a thin layer of spray-on shellac in a well-ventilated area. Let the shellac dry for several hours, and reattach the upholstered pieces of the chair.