Use your garden hose with a spray attachment to hose off the chairs. This will help to remove large debris like old leaves and spider webs.
Fill a bucket with warm water and a small amount of ammonia (a ratio of one part ammonia to three parts water). Dip a stiff, bristled scrub brush into the ammonia-water mixture, and use the brush to scrub the chairs clean. Make sure you turn the chairs over and scrub the undersides too. It's important to use a brush for scrubbing so that you can get into any cracks and crevices to clear out dirt and debris, including dead bug remains and bug eggs.
Place the chairs in a bright, sunny spot to air dry.
Go to your local home improvement store while the chairs are drying, and purchase spray paint in the color of your choice. Make sure you look for spray paint that specifically was created for painting plastic. This type of paint contains special chemicals that help it adhere to plastic better than regular spray paint. This is VERY important. If you ignore this step, you'll end up with chairs that are peeling within a few days.
Apply the spray paint to your completely dry chairs over a drop cloth, per the paint manufacturer instructions. Generally, the instructions will say to hold the spray paint approximately eight to 10 inches away from the surface of your chairs and to spray in a sweeping motion with short, quick bursts. For the best coverage, apply the paint in thin layers, allowing the layers to dry a few minutes between coats. Continue until the chairs are completely covered (including the bottoms).
Allow the paint to dry fully before using the chairs. In most cases, the chairs will be dry to the touch within a few hours, but may take up to a full week to completely cure. While waiting for them to cure, handle the chairs carefully, so you don't end up with cracks in your paint.