Clean the wall where the backsplash will go, and let it dry.
Spread thinset mortar with a notched trowel. Spread on just enough for a few tiles at a time, and place the tiles along the wall. Use spacers to keep them at least one-eighth inch apart. Let this dry overnight. If you need to cut a tile, measure and mark the cut; then, use a blade with a carbide tip to saw through the tiles.
Apply grout to the tile with a float. Wipe off the tiles as you go with a damp sponge. Let the grout dry for a day.
Seal the grout with a tube of grout sealer. Squeeze the tube as you move along the lines.
Cut a piece of a 1-by-4 board o the length of the counter for a 3-D laminate backsplash.
Cut laminate pieces to the dimensions of the board, including the 1-inch edges. Make the 1-inch edges 1/8 of an inch wider so that they stick out over the sides. This will give the 4-inch sides something to butt up against, creating sharp corners.
Spread adhesive to the board, and place the laminate pieces on top. Smooth it down with your hands, and let it dry.
Glue the backsplash to the wall with construction adhesive. Squirt the glue from the tube in a zigzag pattern on the back of the backsplash, and then press it to the wall. While it is still wet, use a level to ensure that it is correctly placed.
Squirt a bead of caulk to the bottom of the backsplash where it meets the counter. Smooth it flat with your finger.
Cut a piece of laminate to the dimensions you want behind the counter. Make the cut with a fine-toothed carbide tip blade.
Spread the laminate adhesive on the back wall with a notched trowel.
Place the laminate to the wall. Press it down with your hand to ensure that it is attached all over. This will give you a thin backsplash that is flush to the wall. It is a good wall cover for places such as behind a stove.