Wipe down the wall where you are installing the backsplash using a tack cloth to remove all dust and debris that may interfere with the adhesive.
Stretch a tape measure from the left side of the installation location to the right side, and note the measurement. Divide the measurement in half to locate the center point and draw a pencil line. If the backsplash is behind a sink, use the width of the sink as the limit, and if the backsplash is behind a stove, use the stove as the width.
Insert a tube of polyurethane construction adhesive into a caulk gun, and cut off the nozzle tip using a utility knife.
Peel off the protective film from one of the thermoplastic squares. Turn the square face down on a work table and apply a zigzag pattern of adhesive over the entire back, but put no adhesive within 1 inch of all edges. Limit the the caulk bead width to 1/4 inch.
Turn the glue side of the square toward the wall and press it to the right of the pencil mark. Press the entire square with a dry sponge, working from the center outward to remove air. Use a slightly damp sponge to wipe away any excess glue that oozed out.
Continue installing additional thermoplastic squares in the same manner, working your way to the right. When you reach the end, move back to the center and begin installing them from the center square to the left until reaching the left edge.
Select a square to begin the second row of the backsplash, but cut a 1/4-inch triangle from the bottom right corner using scissors or a utility knife. Install the square just as you did the others. This notch is required at the intersection of four tiles so they will lie flat and not bulge.
Continue installing each row of squares until reaching the top of the wall or the desired height of the backsplash.
Measure the height of the backsplash and cut two pieces of j-channel trim to the same height. Slide the center groove of one piece over the right edges of the backsplash squares and install the other on the left side of the backsplash to hide the square edges.