There are many fine cleaning products on the market and here is one that deserves a mention. The Kohler Cast Iron Cleaner is a great product which will eliminate stains and minimize scratches.
Just clean and rinse the tub with some baking soda and vinegar to remove any soap scum, then apply a small amount of the cleaner to a soft cloth, apply to spot for cleaning. Be sure to rinse thoroughly and wipe the product dry after each use.
In the rare occurrence of stubborn stains, use abrasive cleaners only sparingly and infrequently. Never use steel wool, wire brushes or abrasive sponge pads. Abrasive products will dull the shine and can eventually remove the porcelain finish.
Keep your cast iron looking new by taking care of scratches or stains as soon as they happen.
Products for cleaning cast iron tubs can be found online or at Home Improvement Stores.