What is the best way to refinish a corian countertop that has scratches?

Sand it out. Basically its like wood. Use fine grit sandpaper 400/ 600 and so on depending how deep the scratches are decides on the grit of sandpaper you st-rat out with.

YouTube - CORIAN REPAIR and RESTORATION (http://www.youtube.com/watch?v=ciaxVe1z9gY)
YouTube - Polishing Corian.AVI (http://www.youtube.com/watch?v=ONn18Rl2EQU&NR=1)

Hi nonnie

I agree with Boat21, also after sanding u can protect counter with a cleaner/polish. U can get it at big box stores or super market. Polish comes in satin or gloos finish.

Good luck

Chuck