As I kid, I used to get paid a $1/screen during the summer, and there was something strangely satisfying of seeing the screen go from coal gray to a lighter shade of aluminum after cleaning them.
1. Before removing the screens, we like to use a Sharpie marker to designate which side of the frame goes up. This way you won't make the mistake up trying to install it incorrectly after you're finished (not that I've made that mistake before...more than once).
2. Fill a large bucket with warm/hot soapy water (a tablespoon of dish detergent will do), and then hose spray the screen flat on a level surface.
3. Use a plastic scrub brush to gently wash clean the screen, being careful as not to tear or dislodge screen material from frame.
4. Thoroughly rinse screens with hose and let dry flat.
5. Wipe clean the screen track of debris and dirt using a paper towel wrapper around a pencil or screwdriver.
6. Pop them back in and enjoy a much clearer and cleaner view.