Purchase a bottle of rust remover. Look for a brand that contains phosphoric acid or chelation agents. Rust remover products are available at home improvement stores, discount stores and supermarkets.
Scrape any surface rust from the antique with an emery cloth or a similar abrasive. Be careful not to damage any surfaces that aren't rusted. Apply a small amount of the rust remover to an inconspicuous place on the antique as a test before cleaning the whole thing.
Place the antique in a bucket of the cleaning solution. Use a plastic bucket so that the cleaner doesn't react with it. If you cannot immerse the antique, then brush the rust remover on its surface liberally.
Leave the antique submerged in the rust remover solution according to the directions on the product label. The amount of time it takes to remove all the rust is dependent on how rusty the antique is when you start.
Rinse the rust remover off of the antique with fresh water. Carefully wipe the down the surface of the antique with a clean sponge to remove any flakes of rust that didn't dissolve.
Return to Step 3 and repeat the process if there are still areas of rust left. It's not unusual for heavily rusted items to take more than one application.
Protect the antique's surface once dry with a rust prevention product to provide long-term protection.