Measure and cut plywood to fit over your cabinet bases using a table saw. Overhang the plywood to the front by 3/4-inch. Align the plywood to the cabinet. Screw through the corner blocks from inside the cabinets into the plywood. Do not allow the screw heads to penetrate the top of the plywood.
Measure the front edge of the counter. Cut the edge trim at 45-degree angles using a miter saw. Apply a bead of carpenter's glue along the edge of the plywood. Place two pieces of linoleum on the top of the plywood to use as a guide. Align the trim with the top of the linoleum. Nail the trim to the edge of the plywood using finish nails every 8 inches. Trim the sides of the counter by cutting one miter edge and one 90-degree edge.
Fill the nail holes with wood fill. Primer the top of the plywood and the back of the trim edging using a linoleum primer designed for floors. Use two coats. This is a goopy primer that seals moisture. Allow the first coat four hours to dry, and allow the second coat to dry for 24 hours.
Test fit your tiles to the top of the counter first. Arrange your tiles. Avoid cuts that produce slivers or very thin tiles. Cut tiles with a utility knife and straight edge. Tile from the front to the back, center toward corners. Peel the paper off the back, and align your tile carefully to the counter. Press your tile edges together for a tight fit. Use a hard roller to press the tile against the substrate in a uniform way.
Router the wood edge last to create a nice edging contour.