Rub the solid-surface cleaner or a product specifically designed for Corian surfaces on the countertops. Rub the sponge over the dull spots and the surrounding areas. Wipe a damp cloth over the counters, removing the cleaner. Dry with a second soft cloth.
Wipe a damp cloth over the dull spots. Rub the counters with an abrasive cleaning pad. DuPont recommends the cleaning pads from Micro-Surface Finishing Products, Inc. Rub the pad around in circular and back-and-forth motions, varying how you rub.
Apply a dab of the countertop polish to the dull spots. Rub the polish onto the dull spots in a circular motion. Apply more polish to the faded areas, placing a smaller amount on the surrounding areas. Keep working the polish into the counter.
Buff the Corian counter with a dry cloth. Remove as much polish from the counters as possible, leaving behind the shine of the Corian. The spots should have disappeared and blended into the surrounding counters.
Repeat the steps if the counters still appear dull or faded. Scrub the faded areas with one of the cleaning pads and apply polish to the surface. Depending on the severity of the marks, you may need several layers of polish before you restore the shine.