In the refrigerator: Store in a single layer in the vegetable bin on paper towels. Or, for longer storage, wrap in foil.
In pantyhose: Take a leg from a pair of clean, sheer pantyhose, drop an onion into the foot, tie a knot and repeat as necessary. Hang in a cool, dry, well-ventilated area. Cut above the knot when ready to use.
On racks or screens: Place on elevated racks or screens, not touching, in a cool area.
In the freezer: For long-term storage, sweet onions can be frozen, but their texture changes so they should be used only for cooking. Chop and place on a cookie sheet and place in the freezer. When frozen, store in freezer containers or bags. To store whole onions, peel, wash, core and freeze in a freezer-proof container or bag.
Drying: Chop and dry in the oven, using the lowest setting. Remove when thoroughly dry but not brown. Store at room temperature in airtight containers.