We have always replaced the screen in storm windows. They are really easy. They have a little gray plastic cord that fits into a groove. When you cut the screen material you just poke the edges into the groove by pressing on the cord. It slides in and the cord holds it into place.
My mom's house has regular wood windows with screens that are able to be removed from the house by way of unhooking them and lifting them up off the hooks on top. If that is the kind you are talking about then the screen material just goes between the frame and the molding. It always looked easy when my dad did it.
Here's a link to DIY that shows how to do it.
http://www.doityourself.com/stry/h2workwithscreens
Another site but with the plastic cord I was talking about.
http://www.hometips.com/articles/repair_window_screen.html
http://blogskinny.com/?How-To-Repair-Replace-A-Window-Scr...
This one is specific to wood frames, it is about half way down.
http://www.lowes.com/lowes/lkn?action=howTo&p=LawnGar...
Have fun!!!
Gina