Place the tip of a silicone caulk applicator against the rip in the screen door. Silicone caulk is available at most home improvement stores.
Squeeze a dab of silicone caulk out of the applicator.
Smooth the caulk against the rip with the back of a plastic spoon or your finger.
Unscrew the screen door hinges from the door jamb using a Philips screwdriver. Leave the hinges on the door, and set it down on a flat surface.
Pry the spline from the groove along the perimeter of the screen up with a flat head screwdriver or nail. Once the spline is removed from the screen door, the screen will be loose. Remove the screen.
Lay the screen down and measure it with a measuring tape. Cut the new screen to match the old screen's dimensions with scissors.
Lay the replacement screen over the entire door. The screen should exceed the perimeter of the spline by about 2 inches on all sides.
Force the new screen in between the groove on the door with the tip of a flat head screwdriver. Make sure you don't tear the screen and it is taut.
Push the spline back down into the groove with the flat head screwdriver so it is flush with the frame. Then rehang the screen door.