First and foremost, pack yourself.
Packing is the number one way to save. Use the proper materials and do not hesitate to ask for advice.
Most people do pack themselves, however in most cases there are a few loose ends for the movers to take care of (i.e.: pictures, glass tops, glass shelves, plants, hanging clothing, lamps and shades). These items add to your cost with both time and material charges. If you plan to transport any items yourself, consider handling these items.