Apply a varnish stripper to the entire table (if applicable). Make sure you get a sufficient amount in any carving or scroll work to loosen the varnish in those areas. Check with a home improvement store to select the varnish that's best for your table's wood type and the kind of varnish you want to remove.
Allow the varnish stripper to dry sufficiently. Use fine sandpaper to smooth the surface and remove any remaining residue. Ensure that all of the previous varnish is gone before attempting to restain. Wipe off the table to thoroughly remove any dust remaining from sanding.
Once the wood is clean, apply the first coat of stain with a fine bristle brush. Use the clean rag to wipe up any excess stain. Allow it to dry.
Repeat Step 3 until the desired shade is achieved. Allow each coat to dry between applications.
Once the final coat is dry, apply a coat of polyurethane or varnish with a clean paintbrush. Continue to apply coats until the desired level is achieved.