Remove any sinks or appliances mounted to the existing countertop, shutting off water valves under the sink before removing. Then remove the existing countertop, using a screwdriver to remove the mounting screws located underneath the counter and lifting it off the base cabinet.
Slide the Corian countertop piece into position, fitting it snugly against any adjacent walls. If more than one length is necessary, place the pieces tightly together and adjust the sections so the front overhang is even.
Measure the length and width of any sink or countertop mounted appliance, then use masking tape to mark a template for each at the counter installation area. Cut an opening out for the sink or other appliance, using a drill to create a starter hole in the corner of the marked template and a jigsaw to cut the full opening.
Secure the countertop to the base cabinet by lifting the sheet up at the front end and applying a line of silicone along the top edge of the base cabinets, then lowering the countertop back down and pressing it lightly into place. If using more than one piece of countertop, join the seams with a tinted epoxy, sanding the seams once the epoxy has dried to give the appearance of being seamless.
Apply caulk or silicone along wall edges and along the edges of any installed sink.