The easiest way to save money on shipping is to plan ahead. If you don't need it there right away, you don't need to pay extra for rush shipments or special handling.
The first pound of any shipment is the most expensive. Whenever possible, consolidate multiple items into larger boxes to save more.
Many shipping companies, including the U.S. Post Office, offer some supplies for free. Good boxes can often be obtained free from local businesses (be careful to avoid boxes used for alcoholic beverages or hazardous substances).
Instead of buying packing peanuts, crumple up plastic grocery bags or inflate zip-closing freezer bags to fill in spaces around your items.