Measure the area, and cut a template to create the design. It's more practical to lay out the design on a template of butcher paper on the counter or floor. You can revise the layout any number of times. It also gives you a chance to cut stone tile ahead of time. Don't forget to leave room for the grout lines. Also, select the placement of any accent tiles at this time.
Cut the stone tiles in the design. You'll need a wet saw with a diamond blade to cut the stone. You can rent these at most home improvement stores, or tool rental stores. The wet saw uses water to cool the blade and prevent the tiles from cracking.
Lay the Stone Tile
Start laying the stone tiles. On very tall vertical areas, you normally begin at the top, but because the area of a backsplash is short, you lay the bottom row first. Use all-purpose mastic for dark stone or white thinset for lighter stone as a base. Apply the thinset with a trowel. Leave about 1/8 inch between the bottom of the tile and the countertop. This will damage to the wall if you replace the countertop.
Press the tiles into place about 1/4 inch from where you want them. Slide them into place to make sure you cover the back of the tile adequately with adhesive, and there's a good bond. There will be some variation in the size of the grout lines if the stone tiles are slightly irregular. Use a level frequently to make sure lines are even. Insert tile spacers to keep the lines even. Clean off any mastic or thinset from the face of the tiles.
Dry and Seal
Allow the stone tiles to dry so they're firmly in place, then thoroughly clean the faces and apply a sealer. Stone tiles have little dips and groves, and are very porous. The sealer makes removing the grout from the face an easier task.
Lay the grout into the grout lines. If the joints are wide, add some sand to the grout to make it stronger. Wipe down the face of the tile after the grout set up for 15 minutes. Clean the faces as thoroughly as possible. The less water used the better.
Wait at least a week before applying the final seal. Clean the face of the tiles again before sealing the area. Use a foam brush to apply the sealer to the entire area. Give several coats to areas that get a lot of abuse, such as behind the stove or sink.