Disassemble your metal lawn chair if possible, so that you can reach the hard-to-reach rust.
Use an orbital electric sander to sand off the rust on a flat surface such as the back of your lawn chair.
Remove the rust from your metal chair legs using a bench grinder with a wire wheel attachment.
Brush the rust off the metal chair parts using a drill with a wire brush attachment.
Use metal files for small, hard-to-reach places on the chair. Sanding cords, sanding blocks, steel wool, and wire brushes all work well for scraping and brushing rust from metal.
Apply naval jelly to the rust, and let it penetrate the area for 1 hour. This product eats away the rust. Flush with water.
Wash down the entire metal chair with mineral spirits and steel wool to completely clean and remove any last traces of rust.