Measure the distance between the cabinet's top board and the ceiling above to determine how much space can be allowed for the cabinet top boards. Cut out 1/2-inch-thick boards of that height and arrange them to fit on top of the cabinets, cutting their lengths to fit their arrangement with each other on the cabinet. Sand the edges of any cuts, then sand the entire surface of each board.
Paint or stain the boards to match the cabinet finish by applying a light coat of paint or sealer with a paintbrush. Apply with the brush strokes moving the same direction as the wood grain, in light, even motions. Repeat as needed to cover all the boards. Allow two hours for the first coat to dry, then reapply with the same process until the color of the boards matches the cabinetry.
Repeat to add three coats of sealant, brushing in the same direction and allowing two hours between coats for the sealant to dry. Let the pieces dry overnight before moving to the next stage of installation.
Position each cabinet top board in place on top of the cabinet. Drill a hole up through the interior of the cabinet and into the bottom of the cabinet top board. Stagger the holes every 6 inches so the boards are evenly attached. Set a 2-inch wood screw in each hole and tighten them securely in place to finish the installation of the cabinet tops.