Remove the wood trim from the doorway if possible. This will make it easier to sand and stain.
Use a damp rag to clean away dirt and debris from the wood trim. Use a mild soap such as dish detergent and water to clean the old, stained wood trim. Dry the wood trim with a dry cloth.
Sand the wood trim. Start by sanding the old, stained wood trim with low-grit sandpaper. The sandpaper should remove the varnish and wood stain from the trim. Use finer grit sandpaper to smooth the wood trim.
Apply a wood stain to the wood trim with a paintbrush. Once brushed on, use a clean rag to remove any excess stain and smooth the color. Allow the stain to dry as the manufacturer recommends.
Apply a coat of polyurethane with a paintbrush. Allow the polyurethane to dry and then lightly sand with fine-grit sandpaper. Wipe the trim with a damp cloth and apply an additional two coats of polyurethane, sanding between coats. Do not sand after the last coat of polyurethane has dried.