Take down the screen. Do not the damage the mesh or bend the frame. Lay the screen against an exterior wall.
Mix a cleaning solution of three parts water and one part ammonia. Substitute dish detergent for ammonia, if desired.
Dip the scrub brush in the cleaning solution and scrub the screen. Turn the screen over and brush the other side of the screen.
Rinse the screen with a garden hose.
Scrub any missed spots and rinse again.
Shake the screen to remove any excess water. Allow the screen to dry completely before returning it to the window or door.