Sand away the existing polyurethane. The bulk of the work can be done with a palm sander, but use 200 grit sandpaper to remove polyurethane from corners and hard-to-reach areas. Take care to remove as little wood as possible.
Clean the area thoroughly. If you are refinishing a floor, sweep and mop before proceeding. Furniture pieces should be wiped clean with a damp rag. Do not use household cleaners or furniture sprays, which could interfere with the new stain.
Apply a new coat of stain, following the manufacturer instructions. Always wear gloves when staining.
Paint the polyurethane on once the new stain has dried thoroughly. Paint on a thin, even coat and follow the grain of the wood. Allow the polyurethane to dry thoroughly -- at least 48 hours.