Cover the entire screen using thick masking tape. Masking tape works better than painters tape because the surface is not as vulnerable as drywall and you need something that will adhere to the screen. Place the tape around all the edges of the screen, on both sides. If you don't have a steady hand when painting, cover the entire screen in masking tape.
Apply a primer to the wood using a bristle paintbrush. Use a primer made specifically for wood and home exteriors. Allow the primer to dry completely before proceeding. Drying times will vary according to the type of primer used. Read the package instructions or wait 36 hours, if in doubt.
Sand the primer lightly with 100-grit sandpaper. Brush away all the sandpaper dust, or use a vacuum to remove it completely.
Apply your paint of choice using a bristle brush. Use paint designed for wood and exterior use. Allow the paint to dry thoroughly, as with the primer, and remove the masking tape.