1 Wipe the furniture down with a cloth moistened with water to remove any surface dirt. 2  Next, moisten a cloth with the chosen cleaner and apply it to the rust stains. 3  Allow it to set on the stain for a couple of minutes.4  Rinse with clean water and a clean cloth.teps to Remove the Rust Stains: 1  Begin by choosing one of the cleaners above, any that you have on hand will work. 2  Wipe the furniture down with a cloth moistened with water to remove any surface dirt. 3  Next, moisten a cloth with the chosen cleaner and apply it to the rust stains. 4  Allow it to set on the stain for a couple of minutes. 5  Rinse with 6  ... I