Soak chrome-plated parts in a bath of citric acid powder (3/4 cup) and water (1 gallon). Rub with aluminum foil, Scotch Brite pad, or toothbrush to remove rust and filth. Then use Nevrdull or chrome polish to finish.
Don’t use steel wool as it can scratch and dull the final finish. White vinegar can be used to soak mounting screws and washers. I have heard of people using the blue Dawn (dish soap) instead of acid, but I have not tried it yet.