Any flaky reddish-brown or yellow "stain" on materials containing iron can easily be identified as rust; especially in wet, cool environments.
Rust can be removed from your bicycle by simply rubbing it away using a steel wool brush and safety gloves to protect from splinters, but other methods include using a light oil or other household items.
Consider using soda pop or a form of citric acid such as lime juice to help lift the rust as you abrasively rub the surface with a fine steel wool brush; these household products are effective, cheap and easy to find.
When using such products as citrus acid, thoroughly wash the area with a soapy towel and water as remaining acid could weaken the metal, according to instructables.com.
Because rust corrodes the metal on your bike, removing it will greatly improve your bike's overall performance, increase the life of your bike chain, and help keep your brake lines up and running.