Corian is the name brand for a solid surface material manufactured by DuPont. It is extremely durable and will withstand a lot of abuse. Over time, Corian does tend to lost its shine and will require polishing. Polishing will also remove any scratches that mar the surface of your Corian. Corian sinks may need more regular polishing than counters due to the fact that they withstand more abuse. DuPont recommends different techniques for different Corian finishes. Sinks are only manufactured in a satin/matte finish and so should be handled according to those instructions.
Fill the sink with equal parts bleach and water and allow it to sit for 15 minutes. This will disinfect the sink and remove any stains from the sink's surface. Rinse thoroughly with clean water. Dry the sink with a towel.
Slightly dampen a piece of 180-grit sandpaper. Sand the sink in a circular motion to remove visible scratches. Work on deep scratches by sanding along the scratch, then going back over the scratch at a 90-degree angle. Repeat this process until the scratch is gone. Continue sanding the entire sink to maintain an even finish. Wipe out the sanding dust with a damp towel.
Switch to finer, 220-grit sandpaper. Sand the sink in a similar motion, sanding all parts to work out any lines left by the coarser-grit paper. Wipe out the sanding dust with a damp towel.
Continue switching to finer and finer sandpapers until the desired shine is reached.
Use a scrub sponge and Softscrub liquid to scrub the inside of the sink. Clean the entire sink. This process will buff the sink, making it look brand new.