Take your mirror outside to avoid getting the dust from sanding in your home. Use newspaper and painter's tape to cover the glass of your mirror. Run the edge of the painter's tape along the sides of the glass while avoiding the frame around it. This will protect the glass while you work on the frame first.
Use sandpaper and apply slight pressure to sand the wooden frame of your mirror on all sides. Remove the old finish completely until the bare wood is exposed. Use a soft cloth to remove the dust particles after sanding.
Apply wood stain that matches the original finish of your mirror's frame to restore its look. Use a soft, dry cloth to apply the stain to the frame. Allow the stain to dry for at least two hours before applying an additional coat to deepen the color to your liking.
Use a small paintbrush to apply one coat of polyurethane, and allow it to dry for an hour. Once dry, remove the newspaper and painter's tape to expose the glass of your mirror.
Spray liquid glass cleaner on the surface of your mirror and use a dry cloth to remove any hint of dirt or streaking. Apply slight pressure on areas that contain dried-on liquids or grime.