Make a paper pattern for the laminate backsplash. Measure the backsplash area and transfer the measurements to the paper. Tape the paper pieces together as necessary. Test the fit of the pattern by setting it in place.
Use the paper pattern to cut out the ¼-inch plywood sheeting for the laminate backsplash. Trace the pattern with a pencil. Cut the plywood with a circular saw. Test the fit of the plywood by setting it in place on the backsplash area. Trim as necessary.
Cut out the seamless laminate backsplash by setting the laminate panel face up on a flat surface. The laminate panel should be large enough to cover the backsplash without seams. Place the paper pattern over the laminate. Trace around the pattern with a pencil. Make the pencil marks slightly larger than the paper pattern. Cut out the laminate sheeting with laminate shears.
Apply laminate adhesive on the front area of the plywood and the back of the laminate sheeting. Let the adhesive dry per the manufacturer's instructions.
Place ¼-inch wooden dowels on the top of the plywood. Set the laminate on the dowels with the glue side facing the glue side on the plywood. One at a time, remove the wooden dowels and push the laminate on the plywood. Smooth it out as you go. Remove the extra laminate from the sides with a router.
Apply construction adhesive on the back of the plywood. Set the plywood in place and push it into the wall so the adhesive can stick to both the wall and the plywood.
Use wood trim to finish the sides of the backsplash, as necessary. Use a miter saw to cut the trim to size and nail it in place with finish nails and a hammer.