Measure the length and width of the cabinet to which you’re installing the countertop using a tape measure. Purchase a sheet of corrugated plastic that’s at least 3 inches longer and wider than your cabinet to use as a countertop design template.
Place the plastic onto the cabinet, against the wall and overhanging all other edges of the cabinet. Mark the edges of the cabinet as seen through the plastic using a black marker, along with the cabinet dividers and corner bracing surfaces. Scribe the rear of the sheet with the line of the rear wall as well, using a compass. Place the compass point onto the wall with the pencil of the compass on the plastic sheet. Drag the compass along the wall to mark a line onto the sheet that corresponds with the shape of the rear wall. Remove the sheet and then cut it along the scribed edge with a utility knife. Place the sheet back onto the cabinet to make certain it now fits tightly against the wall along the scribed cut line.
Create a fabrication form on which to build your countertop with 2-by-6-inch planks. Build a box from the planks the same size as the measured cabinet, cutting the planks to the proper size with a circular saw. Join the corners of the planks together with 10d nails hammered into place. Make sure the top of the plank is level using a carpenter’s level laid across the different boards, before you nail them into place. Place 1-by-4-inch planks flat on their 4-inch sides across the tops of the frame, spaced every 16 inches and nail them into place to serve as a flat level support for your platform.
Purchase the solid surface material in a sheet that’s slightly larger than your desired countertop size. Most countertops overhang the cabinet edges by 1 inch, so purchase a sheet that’s about 2 1/2 inches longer and wider than your cabinet.
Place the solid surface material onto the fabrication form and then place the plastic sheet onto the form as well, with the scribe-cut rear of the sheet completely over the rear of the surface material so that you can repeat the scribe onto the countertop, and the marked cabinet edges centered within the length of the form. Mark the scribe line onto the countertop with the pencil.
Remove the plastic sheet. Cut the solid surface material along the scribed line with a jigsaw, following the penciled line closely to recreate the wall surface in the countertop material. Set the plastic sheet back into place on top of the countertop material, with the rear aligned with the now cut scribed line of the countertop. Clamp the sheet in place.
Mark the actual lines of your countertop onto the plastic sheet with the marker, using a straightedge to assist you in keeping the countertop edges straight. Place the edges so that they overhang the marked cabinet edges 1 inch on both sides and along the counter top front. Cut away the plastic template carefully along the marked edges with the utility knife, leaving the template edge against the countertop. Trace the template edge onto the countertop with the pencil, and then remove the plastic template.
Position a metal straightedge onto the countertop about 1/4 inch in front of the penciled edges to create a rough cut of the countertop. Clamp the straightedge in place using C-clamps on the sides of the straightedge so that you can cut along the front of the metal piece. Cut the countertop using the straightedge as a guide with a circular saw containing a blade specifically manufactured for cutting through solid surface materials. Rough cut both edges and the front of the counter.
Rout the front and ends of the counter to the shaped profile you desire by attaching the chosen profile’s router bit onto a router and then running the router along the edge of the countertop material, cutting the material away until you reach the penciled countertop lines.
Place the template back onto the countertop with the edges of the template aligned with the counter edges. Place any cutout templates onto the plastic surface, using the positions of the dividers and bracings drawn in the template to position the cutouts where they won’t overlap the cabinet construction elements. Trace the cutout template onto the plastic countertop template, and then cut through the plastic countertop template along the tracing with the utility knife. Trace through the countertop template onto the countertop surface with the pencil, and then remove the template. Check that none of the 1-by-4-inch planks extends under the cutout position. If one does, then remove it using the hammer.
Drill through the countertop at one of the inside corners of the drawn cutout using a hole saw placed onto an electric drill. Lower the blade of a jigsaw through the drilled hole on the countertop and line it up with the cutout line. Cut along the line around the cutout marking with the jigsaw blade. Pop out the cutout section of the countertop.
Check the level of the cabinet top with a carpenter’s level. Add wooden shims to the cabinet top to make leveling adjustments so that your countertop will fit levelly onto the cabinet surface. Glue the wood shims into place with construction adhesive and allow them to set for 30 minutes.
Apply construction adhesive to the top of the cabinets every 6 inches. Set the countertop in place, and allow the adhesive to cure for 30 minutes.
Smooth the countertop using a random orbital sander and 120-grit sandpaper. Smooth it even more by going over the countertop a second time with 220-grit sandpaper. Wipe the residue off with a tack cloth.
Follow the sink manufacturer’s instructions for its installation, as different sink types will require differing techniques.