Remove the clock handles to access the plate, and then unscrew the plate from the clock using a screwdriver. Pull the plate free, then place the plate onto a level work surface.
Dampen a piece of soft lint-free cloth in water and use the cloth to clean the surface of the clock plate. Clean any detailed areas with a cotton swab. Pat the surface dry with a dry piece of cloth before continuing.
Dab a piece of cloth with brass cleaner, then rub the cleaner over the entire surface of the clock plate. Use light pressure during the cleaner application to avoid damaging the plate in any way. Allow the brass cleaner to dry to a slight cloudy haze on the brass for about 5 minutes.
Buff the haze away with a clean cloth using small circular movements until the brass begins to shine again. Change the cloth when it begins to grow dark with removed tarnish.
Wipe the surface of the brass plate with a cloth dampened by lacquer thinner to remove any polish remnants.
Screw the plate back to the clock face and then replace the hands.