Galvanized steel is designed not to rust, so if you have a galvanized steel item that has rusted, it means that the galvanization has worn off completely in those areas. Galvanization involves zinc, which corrodes instead of the actual metal to prevent rust. When the zinc is all gone, this is when real rust sets in. You can remove rust from galvanized steel, but you will need to repair the area that rusted to prevent the rust from simply returning when the metal is again exposed to moisture.
Clean the galvanized steel. Wipe down small pieces of steel using cleaning rags with three drops of liquid detergent in order to remove dirt, dust, grime and sometimes large chunks of rust. Larger items can be pressure-washed or hosed down. The point is simply to remove grime so that you can target rusted areas more specifically.
Scrape off large areas of rust with the wire brush. Use firm pressure and a back-and-forth motion to remove rust from the metal. The wire brush may scratch the metal, but since you will have to paint and re-galvanize it anyway, this is OK. Wear your protective goggles from this point forward to keep rust particles from flying into your eyes.
Sand off any remaining rust. Use firm pressure and rub the sandpaper back and forth just over the rusty areas. Do not sand the entire item unless the entire thing is rusty.
Clean off the rust dust. Use the hand broom to dust off all the rust particles and to clear the area to be sure that there is no more rust. Wipe down the area with a damp cleaning rag and three drops of liquid detergent, then dry it completely to prevent the formation of flash rust in the exposed areas.
Take preventative measures to inhibit further rust. Paint the item (or at least the sanded and scrubbed areas) with zinc-rich paint or cold galvanizing spray to restore the galvanization to the steel. Apply two to three coats of paint, but be sure to allow at least 90 minutes between coats to insure that the area has dried completely.