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First, place loose or small parts in plastic bags, seal them, and (this is the important part) label the bags clearly. If possible, remove any breakable parts (for instance, vacuum tubes in an antique radio) and wrap them separately. Bundle the cords with rubber band or twist-ties and label them if needed.
If your piece has a large amount of empty space inside the chassis (as, for instance, in an older television set), LOOSELY fill this space with bubble wrap.
Cut a piece of bubble wrap to fit over any glass screen, and tape it in place before wrapping the entire piece in several layers of bubble wrap. When you're done, you may want to label the top of the piece unless this is obvious. Pack as you would any fragile shipment.