Retighten any screws or bolts holding the table legs to the tabletop. Apply fresh wood glue to any mortise-and-tenon joints on the table legs or the chairs. Clamp any newly glued parts together with furniture clamps or nylon roping. If the table and chairs were purchased in a fully disassembled state, dry-fit the parts together to make sure all the parts are present.
Apply the wood stripper and remove old paint, varnish, or stain from all surfaces of the wood, including the undersides of tabletops and chairs. Work in small sections, a little at a time. Avoiding using a paint scraper tool since this can damage the wood grain. Use steel wool and stripping pads instead.
Sand the table and chairs with fine-grit sand paper after stripping is complete. Don't use a power sander as this could damage the wood grain. Use a tackcloth to remove all traces of sawdust from your project.
Reassemble the table and chairs if necessary. Use wood glue to rejoin any mortise-and-tenon joints and apply furniture clamps to all pieces. Be sure to "catch" and remove any glue drips while the glue is still wet. If you don't have clamps available, use nylon ropes to bind the pieces together, very tightly. Let this glue dry for several days before releasing the clamps or the ropes.
Apply wood stain, using a soft rag or stain brush. Work with the direction of the wood grain, not across the grain. Apply the stain sparingly at first; you can always apply more stain, or let the stain come into contact with the wood longer, for a darker color, but you can't reduce the darkness of stain once it has been absorbed by the wood. Apply one thin coat of stain, wiping away any excess stain with another clean, soft cloth. Let the stain dry completely.
Apply a finish coat such as a clear satin polyurethane product. Use a high-quality brush and watch for errant brush bristles left behind in the finish coat. Allow it to dry.