Rub the table with a rag dampened with denatured alcohol to remove a shellac finish. If the finish isn't shellac, paint the table with a thick coat of paint or lacquer stripper to remove a lacquer or varnish finish and any old paint. Allow the stripper to sit for the time specified on the package, then use a scraping tool to remove the stripper and finish.
Sand the table with 100-grit sandpaper to remove any remaining finish, paint or stain. Wipe the table free of dust and debris with a wet rag. The table must be completely bare to take paint.
Paint the table with a latex or oil primer, moving along the grain. Use a nylon brush to apply latex primer or a natural bristle brush to apply oil paint. Allow the primer to dry before proceeding. Drying time will vary depending on the type of paint used.
Paint the table with a latex or oil paint using the same methods used to apply the primer. Allow the paint to dry, and apply one or two additional coats for better coverage if desired.
Paint the dry table with lacquer to protect the table from scratches and moisture.