Put the upholstery tool on the vacuum cleaner, and vacuum the screen. Remove the upholstery tool, put on the crevice tool, and vacuum the corners and ridges around the screen.
Loosely roll the bath towel into a log shape, and place it at the base of the screen door to catch any excess water that runs down. This will make clean-up a little bit easier when you are done cleaning the door.
Pour the water and detergent into the bucket, and gently stir the cleaner with the soft cloth and your hand.
Wring the excess water out of the cloth and wipe the door, starting at the bottom of the frame and working your way up. Wet the cloth again when it starts to feel dry. The screened portion of the door will require more water and cleaner than the door frame.
Rinse the cleaner out of the cloth, and fill the bucket with clean water. Wipe the screen door with the clean water to rinse off the detergent. Remove the bath towel, and allow the screen door to air dry.