Get a Scotch-Brite heavy duty (green) scrub sponge and a can of Bon-Ami cleanser. In the sink especially wet the bottom of the sink, sprinkle some Bon-Ami in the bottom, and scrub with the Scotch-Brite until clean. It should look like new unless there are scratches or chips there. You can also use a chlorine bleach diluted with water to disinfect the sink. It will get down around the drain ring where it's difficult to clean. Bleach will not harm the Corian. Cleaning the countertop will depend on the level of finish. If it's a light color with a matte finish use the green Scotch-Brite. Bear in mind this may make it appear dull if there's much sheen on it. If it's a darker color with a satin or semi-gloss finish you may need to use a white Scotch-Brite (non-abrasive) with Soft-Scrub to avoid dulling the surface. If there are surface scratches it may pay to have a fabricator come in to completely re-sand the top to a uniform sheen. This will make it look like new. Also check to see when it was installed as it is covered by a 10 year installed warranty which protects against product, fabrication, & installation defects (not customer abuse such as scratches or minor chips).