Get a can of Electro-Sol. It comes in a spray can and is great for cleaning corrosion and contacts. It is supposed to be safe for paints and plastics too, but try not to get it on the paint anyway. Then use the dielectric greeze as Phil said. The grease is also called "bulb grease" in some auto stores, same stuff. It looks and feels like vaseline, the stuff Michael Jackson uses, and you just put a dallop of it on all your electrical connections and in all your plugs. It keeps water out and makes the contacts good as new, forever.
