Combine a 2-gallon bucket of water with 1 tablespoon of dish soap. Dip a soft, non-abrasive rag into the soap and water mixture and lightly scrub the dirt off of the chrome. This is a light method for cleaning chrome that is not very dirty.
Mix a 2-gallon bucket of water with 1 cup of vinegar. Dip a soft rag into the mixture and scrub the chrome. This mixture works better for dirtier chrome since the acidity helps to remove the tarnish. Sprinkle baking soda on the rag to bump up the cleaning power.
Crumple up a piece of aluminum foil and apply vinegar to it. Scrub the chrome with a medium amount of force. Do not to scrub any harder than this to prevent scratches. This removes stubborn rust from the chrome and is optimal for cleaning objects like bikes and bumpers. You can even substitute the foil with a very fine grade steel wool. Rinse the chrome off with water and dry it thoroughly so that new rust does not form.