I have replaced screening before. It’s any easy job anyone can do. You need a spline (the rubber stuff that holds the screen in the frame), a spline roller, and screen. The spline and the roller will cost you about $3 or $4 and a roll of 36″ by 25′ fiberglass screen should be around $15.
Family Handyman has a great how-to at http://www.familyhandyman.com/DIY-Projects/Doors—Windows/Window-Repair/how-to-fix-a-window-screen/View-All. I can’t do a better job than they did so I will refer you to that for instructions. They had the great suggestion of putting a brick in the center of the screen so you don’t get it too tight and warp the frame. I used heavy books instead.
Just be careful when you’re cutting the excess screen off and don’t slice your finger like I did…
This is one of my almost completed screen — I have one side left to cut the excess screen off. You can see the books I used as a weight over to the right and the left over spline to the left.
The screens look great and I can open the windows now 🙂