Hi Mar: Here is a site that has some questions and answers regarding ScreenEze that might be worth a read:
This site tells about how to build the screened in porch, but if you zip down to #21, it tells how to attach the screen, finally! :)
Best way is to make a wood frame to fit from post to post of the railing. Staple the screen on the frame and screw the frame to the railing. This way you only have a few holes to fill if you ever remove the screen.