Put on your rubber gloves and clean the wire of any dirt or grime by washing it with some soap and water and a cloth.
Soak another cloth in hydrogen peroxide, hold it in one hand while pulling the zinc coated wire through it with the other hand. Hydrogen peroxide breaks down the layer of oxidization on the surface of the zinc. Depending on the quantity and severity of the oxidization, you may require further cleaning.
Soak a ball of fine steel wool in hydrogen peroxide and repeat the same method as in Step Two, pulling the wire through the steel wool. Take care not to scrub the wire too hard, as often the layer of zinc coating is thin, and you do not want to remove it.