Use a utility knife and a flat-head screwdriver to remove the damaged window screen. You will need to remove the spline from the frame before you can remove the actual screen. There will be a small amount of dirt and debris in the channel. Be sure to clean it properly before moving on to the next step.
The new screen material should be at least a couple of inches wider than the window frame. Trim the screen material length wise with a utility knife. As with the width, the length of the screen material should be 2 inches greater than the length of the frame.
Carefully roll the screen in such a way that it completely covers the frame.
You will now need to tape the screen in order to temporarily hold it in place. While you are taping the screen to the ends of the frame, make sure that the screen is pulled tight.
Use the convex wheel (wheel with the rounded edges) of a screen roller in order to push the screen into the channel by rolling the screen over the new one.
To secure the new screen in place, you will need to use a new screen spline. Push the spline into the channel so that it prevents the screen from coming out of the channel by means of the concave wheel of a screen roller. To prevent the screen from popping off, make sure that the spline is pushed as far into the channel as possible.
To complete the task, trim off any excess screen material.