Place your plywood substrate against the wall where you intend to install the backsplash. Check to ensure that it fits snugly into the backsplash space.
Cut a piece of laminate using the plywood substrate as a template. Ensure that the laminate piece is slightly larger than the plywood on all sides. This gives you an error margin when gluing the laminate.
Lay the plywood substrate on a flat surface. Spread an even layer of laminate glue on the surface of the plywood. Let the laminate glue dry until it becomes tacky.
Lay the laminate backsplash face down on a flat surface. Spread an even layer of laminate glue on the back of the laminate. Let the glue dry until it becomes tacky. Apply the glue to the laminate immediately after applying glue to the plywood substrate to ensure that both pieces are ready at approximately the same time.
Place a series of long, thin dowel rods approximately 6 inches apart across the tacky side of the plywood. The ends of each dowel rod should stick out from the edges of the plywood.
Lay the sheet of laminate, glue side down, on top of the dowel rods. Do not press down on the laminate. The dowel rods merely allow you to line up the laminate with the plywood.
Pull each dowel rod out from between the plywood and laminate, which will let the laminate slip perfectly in place over the plywood substrate. Roll the laminate sheet flat with a roller.
Turn the plywood substrate over, laminate side down. Cut away excess laminate from the sides of the substrate with a utility knife. Attach the laminate backsplash to the wall with screws.