Set two 36-inch two-by-four boards parallel to each other with their large sides down. Space them 12 inches apart. Set two 12-inch two-by-four boards between them, perpendicular to them with their large surfaces down as well. Slide the shorter boards to the ends of the larger boards to make a 19-by-36-inch rectangular frame.
Drill 2 holes through each long board and into each end of the shorter boards. Set 5-inch wood screws in the holes and screw the frame together.
Repeat with two more short boards and two more long boards to create another identical rectangular 19-by-36-inch frame.
Set four 6-inch two-by-four boards up on their ends in a 19-by-36-inch rectangle. Set one of the rectangular frames on top of them and adjust the short boards so they are flush with the longer sides of the frame. Drill two holes through the frame and into the end of each short board. Attach the boards together with 3-inch wood screws.
Flip the frame with attached short boards over and set the other rectangular frame on top of it. Drill two holes through the frame and into the end of each short board. Attach the frames together with 3-inch wood screws.
Position four additional 6-inch 2-by-4 boards between the rectangular frames, evenly spaced along each pair of side boards. Attach them to the frames in the same manner as the corner short boards.
Set a countertop that measures at least 1-by-24-by-36 inches upside down on the working surface. Set the frame on the countertop so that one side of the countertop overlaps the frame by an inch and the other side overlaps the frame by 11 inches. Drill holes down through the frame and into the countertop every six inches. Attach the frame to the countertop with 2 1/2-inch wood screws.
Position the frame and countertop on top of the counter where they will be installed. Drill up through the bottom of the counter and into the frame. Attach the frame to the installation counter with 2 1/2-inch wood screws.
Cover the exposed frame sections with two 1/2-by-9-by-36-inch plywood boards and two 1/2-by-9-by-20-inch plywood boards so all the frame is covered. Screw these boards in place with 2 1/2-inch wood screws.
Cut backsplash tile to fit these side surfaces. Apply mortar to the plywood boards and position backsplash tile on the surfaces. Allow the tile to dry and caulk any exposed areas or corners.