Loosen the hinge screws with a screwdriver and remove the door from the frame. Lay the door on a flat, hard surface where it is convenient to perform the repair.
Pry out the old spline from the groove where the screen is attached. A corner is a good place to start. Once you have a couple inches of spline pulled out, you can pull out the rest by hand. With the spline removed, the screen will detach easily.
Measure the length and width of the area for the screen. Add 4 inches to the measurements so you have overhang of screen on all sides.
Position the screen on the door so there is an even overlap on all sides. Ensure the screen is centered on the door and is flat against the frame.
Start at a corner and press an end of the spline into the groove of the door on top of the screen. This will trap the screen in the groove with the spline on top of it. Ensure that the spline is stretched out and has no slack.
Roll the spline tool over the spline to press it into the groove in the door on top of the screen. As you work the spline into the groove, ensure that you keep the screen smooth and without creases or wrinkles.
Cut off the excess screen with a utility knife. Rehang the door in the door frame.