Install a tube of clear silicone adhesive into a caulk gun. Trim off approximately 1/4 inch from the tip of the nozzle using scissors.
Squeeze the trigger on the caulk gun to dispense the silicone adhesive on top of the cabinet base edge in a quarter size dab. Repeat the process around the entire perimeter of the cabinet top every 12 inches.
Pick up the Corian countertop with the help of another person and hold it over the cabinets until you have it flush with the back wall and the sides are in the proper position. Lower the counter to the cabinet and press firmly secure it to the adhesive.
Attach the short Corian backsplash to the counter by applying a ¼-inch wide bead of silicone along the bottom of the backsplash and pushing it into place on top of the counter back.
Wipe off any adhesive that oozes out using a damp rag. If needed, apply 1 to 2 tbsp. of rubbing alcohol to the rag to speed the removal. Allow the silicone to dry.
Apply another 1/4-inch bead along the seam where the backsplash and the counter meet.