Prepare the existing countertop surface by sanding it smooth and clean of any surface gloss. Wipe off the dust.
Mark a straight line across the middle of the countertop, from front to back, using your carpenter's square and pencil. The line should extend down over the front edge of the countertop.
Cut granite tiles on your wetsaw to hang on the vertical front edge, cutting them the same height as the height of the edge (generally, about two inches).
Spread mortar on the backs of the tiles with your trowel and press them into place, one at a time, along the front edge. Put spacers between them. Cut the pieces at the edges as needed, on your wetsaw. Press your level across the tops of the tiles to ensure they're even.
Spread mortar on top of the counter, with your trowel. Press the first row of tiles into place along the front span of the top, at the center line and sitting far enough forward to cover the sides of the vertical tiles hanging over the front. Set spacers between the tiles. Use your level to press them even.
Set the rest of the tiles in the same manner, in a grid pattern, working off the center line and back, and putting spacers between all of them. Cut end pieces as needed with your wetsaw. Use your level to even the tops of the tiles.
Mark your backsplash area on the wall with your pencil and square. Spread thinset mortar over the wall within the marked area and press tiles into place, using spacers as before. The tiles on the backsplash should line up with the tiles on the countertop. (Note: Put spacers between the bottom of the lowest row of backsplash tiles, where they meet the countertop, so there's a space.)
Let the mortar set overnight. Pull out the spacers.
Spread grout over the backsplash and countertop with your grout squeegee, pressing it into the spaces between the tiles. Don't grout the space where the backsplash meets the countertop, but grout the rest. Use a damp sponge to wipe up excess grout. Let it set for a day.
Run a thin bead of caulk in the space where the backsplash meets the countertop.