Warm water to get rid of salt and anything else that's soluble. Vinegar to remove basic copper carbonate, ammonia to remove cuprous chloride. I'm not really sure what it'll be. You'll need plenty of ventillation for the ammonia though.
The stains are there for a reason - that there is some water seepage.
One seacock on Forethought was particularly green. The spigot fitting on the outlet snapped off in my hand when I gave it a push. It had corroded through, due to de-zincification.