Measure the space where you want the back splash. Note the size and position of any electrical outlets or other permanent objects.
Draft an outline of the space on a large piece of paper. Set the tiles in the draft and figure out the best layout for the space.
Prepare the wall for tiling by washing it with trisodium phosphate, rinsing and drying it. Remove any electrical plate covers so the surface is completely clear.
Apply premixed tile adhesive with a notched trowel. Work in small sections, about 2-feet-square, so the adhesive doesn't dry before you use it.
Press the tiles into position on the adhesive. Use a level to ensure they're straight. Continue applying tiles until the surface is covered. Allow the tiles to set for at least 24 hours.
Mix grout with water in a bucket according to the package instructions. The grout should be as thick as toothpaste and lump free.
Scoop the grout out onto a smooth trowel and apply it over the tile, holding the trowel at a 45-degree angle from the wall. Cover all the tiles.
Buff off any excess grout with a damp sponge. Dry the tile with a cloth.
Fill the crack where the tile meets the counter with a mildew-resistant caulk. If the back splash runs behind the stove, you won't need to do this.