Stand green onions upright in an inch of water in a tall container covered loosely with a zipper-lock bag. Put in the refrigerator. When stored this way, with a water change once every 3 days, green onions can last for well over a week with very little loss in quality. Remove the rubber band that are likely keeping the stalks together, and don't wrap a rubber band around the plastic bag. That will trap in moisture and cause your scallions to wilt more quickly.

Alternatively, you can store green onions in a breathable bag in the high humidity drawer of your refrigerator.