Packing all boxes ahead of time is a big cost saver. Having all your boxes well organized and labeled (on all sides of the box) also make packing and unpacking easier. And if you're paying by the hour, this saves you cash.
When gathering boxes to pack for your move, be sure to find ones strong enough for the task. Moving boxes provided by moving companies have double walls that can support the weight of other boxes and furniture stacked on top of them. If you use single-wall boxes, the sides could crumble, damaging your goods inside.
Disassembling furniture is another way to save money. Pro movers will usually disassemble furniture for you, but if you're able to take things apart yourself, it can cut back on the number of labor hours you pay for.
Related: Where to get moving boxes near you for cheap (or possibly free).