Measure out the dimensions you want for your backsplash on the wall, marking it out with a pencil and level.
Mark an X through the middle of the marked area with the tape measure, square and pencil. The two lines of the X should be exactly perpendicular to each other at the intersection. If the backsplash is rectangular rather than square, the ends of the X won’t land in the corners of the backsplash, but will be short of the corners. This is OK.
Spread tile mortar over the marked area inside, using a notched trowel. The lines of the X should be visible through the mortar.
Press one square wall tile to the wall at the middle of the X, in one of the four corners created by the intersection of the two lines there. Align two adjacent edges of the tile to the two lines, so the tile is tilted at 45 degrees.
Press additional square tiles in place alongside the first one, along the lines, working your way outward from the center toward the edges. Put spacers between the tiles as you hang them.
Hang all the full tiles that will fit in your marked area. Go back and cut tiles on your tile cutter for the remaining spaces along the backsplash perimeter. The spaces will be triangular, meaning your cuts will have to run diagonally over the tiles. Set the tiles with the cut edges lined up with the outer perimeter of the marked area, and the finished edges of the tile alongside the neighboring tiles.
Use your notched trowel to spread mortar over the back of each trim tile, and press each one to the wall alongside the cut edges of the tiles at the perimeter of the backsplash. Put spacers between the cut tiles and the trim tiles. Border the whole edge of the backsplash with trim tiles.
Let the mortar set for 12 hours. Pull out the spacers.
Spread grout over the tiles with a grout float, pressing it into the spaces between the tiles. Wipe up the excess grout with a damp sponge.
Let the grout set 24 hours. Caulk the line between the base of the backsplash and the countertop.