The amount of money spent moving depends a lot on what you are willing to do and how much time you leave to plan. You see, when moving the only thing that really matters is that you get all your property from point A to point B intact and undamaged. The more effort you spend planning out your move and the less help you hire, the cheaper it is. Then again, this inexpensiveness comes at a price. You will have a lot more work and you might have to take a few risks.
For short-distance moves, it is often possible to rent a small van and make several small trips between two properties.
One of the easiest ways to save on moving is with used moving boxes. The more organized you are at packing, the easier it will be for you to save money. Most over your possessions can probably be moved in free boxes that you can get outside of stores. A lot of grocery stores go through literally hundreds of cardboard boxes in a week. Usually, they will be perfectly willing to give them to you for free if you ask. Although these are not great used moving boxes for heavy or valuable possessions, for most of the routine transportation that you do they will work just fine. They are small enough to be easy to handle, and they are fairly solid as well.
Then again, sometimes it makes more sense to invest in higher quality used moving boxes. This is especially true if you have a lot to move. Going and getting boxes from grocery stores is fine for a small household, but for a larger move you want your boxes to all be of the same size. This makes it much easier to stack them and guarantees that they will not shift around on the way over.
Besides used moving boxes, there are a lot of other shipping and storage supplies that you can get for your move. A lot of people I know like to move in stages. They put their most important and needed possessions in used moving boxes and take them over to the new house. They leave their less important stuff in storage until they start to get settled. Then, one trip at a time, they start to bring things out of storage and over to the house. This stops things from getting cluttered and makes the transition to living in the new place that much easier. The trade-off is that it takes longer to do. Overall, it is probably more involved and more work. Still, it does let you start living in your house immediately without the worry of additional clutter.