I have several cultured marble countertops in our home. They are about 10 years old, does anyone know how I would get rid of them? I'd like to do this myself. :)

Your title and your question aren't really the same. If you want to get rid of them hit them with a hammer and remove the pieces. If you meant the stains that's different. Cultured marble is made from marble dust anresin and is highly stain resistant. Try buffing with an automotive buffer using polishing compound. If that fails lay a paper towel over the stain and soak the towel with bleach periodically for about a half hour, then buff again. Do not use buffing compound, use the finer polishing compound, it's a different grit.