Mark the dimensions you want for the backsplash, using a pencil and level. Mark a vertical line through the center of the backsplash area, from top to bottom.
Spread tile adhesive on the wall, within the marked area, using a notched trowel. Your center line still should be visible through the combed pattern of the adhesive.
Set the first tile to the wall, at the bottom of the area, on one side of the center line. Build out toward both sides with other tiles, pressing them in a horizontal course along the countertop. Put spacers between the tiles, and below them to separate them from the counter.
Cut the tiles, using the tile cutter, at the two ends of the course to fit within your marked out area. Hang the end tiles with the cut sides running along the two vertical end lines of your marked out area.
Press the second course of tiles in place above the first, again starting at the middle and working to the sides. Cut the end tiles as needed. Repeat, working up the wall course by course, putting spacers between all the tiles. Fill the whole area.
Let the adhesive dry for 24 hours. Remove the spacers.
Measure the top span of the backsplash and transfer the measurement to a piece of trim. Cut the trim to that size on your miter saw, setting the saw at 45 degrees inward for each cut (so the top edge of the piece is longer than the bottom edge, with the bottom edge being the length of your backsplash). Set the trim along the top of the backsplash, so the two mitered corners jut up and out from the two upper corners of the backsplash. Put spacers between the trim and the tiles. Secure the trim with your trim nailer.
Repeat the process of measuring, cutting and hanging trim for the two vertical sides of the backsplash, mitering the upward-facing ends and straight-cutting the downward-facing ends (which will be sitting flat on the countertop). The mitered upper ends of the side pieces should abut the mitered ends of the top piece, forming the corners of the frame.
Grout the backsplash with a grout float, scraping the grout over the tiles and pressing it into the spaces. Don’t grout the joint between the tiles and the wood trim. Let the grout set for 24 hours.
Caulk the space between the tiles and the wood trim. Also, caulk along the bottom of the backsplash, where it meets the countertop.