Buy Evaporust from auto store. Soak some paper towels in it. Wrap the paper towels around the frame and make sure it is touching the frame(no air bubbles) where the rust is. Cover the frame with a trashbag to keep the paper towel from drying out.
Let it sit there for 2-10 hours depending on the rust. Rinse with water and dry. It should remove rust, grease, dirt, etc. If its really deep rust, you can unwrap it and rub the spot with a towel after 5ish hours to remove some of it and let the rest come off easier then.

Use nail polish or an auto paint pen(auto store) to match the color and to get small spots. Paint pens work great for small chips. You need to remove the rust before painting. If you paint over rust, the paint wont adhere permanantly and the problem will just continue.

The evaporust can be reused over and over.