Put on your safety goggles and particle mask. Use your power sander and 80-grit sandpaper to buff and dull the surface of the existing laminate. Get it so that it no longer reflects light from any angle.
Measure each area of the countertop. Mark the measurements on your laminate sheets, then add 1 inch on all sides. Cut out the sheets using your router with laminate-cutting bit.
Lay the cut pieces of laminate upside down on spread-out newspapers. Brush contact cement over the backs of them. Brush contact cement over the surface of the countertop. Allow the contact cement to air-dry according to the instructions on the packaging (generally about 10 minutes). Note: Even though the contact cement won't feel sticky to the touch, the treated pieces will bind to each other if you accidentally allow any two of them to make contact.
Apply the front vertical edge piece of laminate first. Hold the piece steadily in front of the area where it's going to be mounted, get it in position, and press it to the surface. The laminate should overhang on all sides by about an inch. Run your roller over the piece to secure it. Use your router to trim off the overhanging laminate along the corner edges of the countertop.
Lay your 1-inch dowel rods down over the top span of the countertop, from front to back, spacing them about every foot. Set your large top piece of laminate over the rods, so the rods separate the piece from the surface of the countertop. Get the piece correctly positioned, then slide the rods out one by one, starting at the middle. As you slide them out, press down on the laminate. Once the new laminate is completely down, run your roller over it and trim the edges with your router.