Turn a stud finder on and place it against the left side of the wall where you are installing the backsplash. Slide it to the right until a light appears, which signifies the presence of a vertical stud behind the wall. Draw a small line on the wall with a pencil to designate the stud locations.
Continue sliding the stud finder across the backsplash installation area, marking each stud location with the pencil.
Measure the length and the width of the installation area with a tape measure.
Place a piece of backer board on a work table and draw an outline on it for the backsplash with the above measurements. Use the tape measure to designate the length and width of the backsplash and mark these with small pencil lines. Connect each of the lines with a straightedge.
Plug in a circular power saw and put on safety glasses. Slide the backer board to the side of the table so one pencil line hangs off it. Cut through the pencil line with the saw. If needed, clamp the backer board to the table with table clamps. Turn the board, as needed, until you cut out the entire outline of the backsplash.
Place the board up to the wall in the desired installation area. Line up the left side of the board with the leftmost wall stud mark.
Insert 2-inch long screws or nails through the backer board in the location of the leftmost wall stud. Insert additional nails or screws every 4 inches until you reach the bottom of the backsplash area. Insert screws or nails in each remaining wall stud location, using the same spacing.
Install a second piece of backer board next to the first one, if necessary, to cover the entire backsplash. Once installed, apply mesh tape to the seam between the two board pieces.