Chemically, acids are the preferred way to remove rust stains. Believe it or not lemon juice (citric acid), or the "stronger" white vinegar (acetic acid) are mild ACIDS which may resolve the problem. In the corner of an affected area, I would test both acids to determine which one is most effective. Apply the acid with the clean sponge side of a white, nylon scrub pad backed sponge (available at supermarkets). Agitate with the scrub pad side. Rust stains are the result of oxidation. Rinse thoroughly afterwards and blot dry.
Another method on clothes is to try a waterless hand cleaner like Goop or DL. Just work it into the spot, then wash it. Test an inconspicuous spot first to make sure it doesn't fade the fabric. A member who had rust stains on a pair of white pants cleaned them using hand cleaner and a nail brush.
NOTE: Always test an inconspicuous area for colorfastness, etc. before treating the exposed area. Also note that certain stains are permanent.
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This article has been contributed in part by Michigan State University Extension. For more cleaning and stain removal tips and hints, please visit our cleaning community forum where experts are ready to help answer your questions.