Scrub the furniture lightly with a stiff brush to remove any loose dirt and rust. Use sandpaper or a small scraper to remove as much of the rust as you can without scraping the paint off of the furniture.
Mix together a few tablespoons of baking soda with a teaspoon of vinegar to make a thick paste. Apply this to the furniture and allow it to sit for a few minutes. Or you can apply a thin layer of lemon juice if you prefer.
Rub the area with a soft sponge to loosen any remaining rust. You may need to apply several coats of lemon juice or the baking soda paste to remove all traces of rust.
Rinse the furniture with warm water. Gently rub the furniture with warm soapy water to neutralize the cleaner.
Repeat the process as needed until all of the rust stains have been removed.
Repaint the furniture with outdoor paint in order to prevent future rust.