It all depends on the severity of the problem. Sometimes you have no choice but to either re-chrome the part or replace it. 000 or 0000 steel wool using a car wash/water mix for a lube will remove rust but will leave some fine scratches in the finish. That requires using a liquid or paste polish (white compound or Jeweler's Rouge) with a power buffer to remove the scratches and restore the finish to mirror like qualities.
Using something as simple as an old toothbrush or brass brush and household cleanser also works to remove rust from chrome (cleanser is a mild to fine abrasive). Toothbrushes are usually used in "hard to get at" areas like creases or folds in the metal. A "Dobie" pad or "Mr. Clean Magic Eraser" will not scratch any surface but can clean the rust off with just a car wash/water mix.
Buy a good chrome polish. Mother's Chrome Polish is available at most local auto store chains. Most chrome polishes will contain/leave a protective coating on the chrome. Can apply wax to the chrome after a day or two for even more protection. The reason I recommend waiting a day or two is in case one has to do some touchup polishing. Some chrome polishes contain "fillers" that hide imperfections, but it depends on how anal you are about it (perfectionist).