Remove the old lattice with a flat pry bar. Cut the lattice into pieces if it is large and awkward to remove in one piece.
Measure the space where you will be placing the new lattice; leave room for a frame if you are using one. Measure your new lattice and cut it to the desired width and height using a circular saw or sabre saw.
Drill a clearance hole with a drill bit slightly larger than your screw's diameter at each location where the lattice meets the frame or support pieces; this will give your lattice room to expand and contract without cracking.
Place your washers on your 1-inch panhead screws and screw your new lattice piece onto the frame or support pieces with a Phillips head screwdriver, inserting a screw at each clearance hole location.