For very dirty or very rusty surfaces, use vinegar or another mild acid suggested below, then follow up with foil.
Dip the aluminum foil in water again whenever it gets dry. If you are working on a severely pitted surface then try wadding up the piece of aluminum foil. The edges that this creates will help to smooth down the metal and will actually fill in the pitted rust areas.
Be sure to apply a coat of polish or wax on your clean chrome to prevent more rust from forming.
Diet cola does not have sugar in it, so the process will be less sticky. However, the sugar does help the acid to adhere to the rust. Avoid strong or concentrated acids, which can etch and weaken the underlying metal. If these household acids are ineffective, try again with phosphoric acid, but keep a fan on to blow corrosive fumes away from your face.
Apply a coat of polish or wax on the chrome to prevent rust from forming in the future.
If the dirt is very difficult to remove you can also use vinegar to clean the surface of the chrome. Vinegar is a mild acid and will help in the process of rust removal as well.
If the area gets dry then be sure to add more oil or chrome polish. Rubbing dry chrome with metal wool will scratch and damage the surface.
Make sure to put a coat of polish or wax on the chrome to keep the rust from reforming. If extra care is needed, check out the followup section below.
Typically, wax is applied, buffed and left to dry, then a second layer is applied over it and buffed again.
