You have several options.

To get a baseline of how much you might pay, talk to a few moving companies and get moving quotes – have them see exactly what you need moved so you get an accurate estimate. (Don't assume it's too expensive -- with the economy the way it is, many quality moving companies are eager to pick up any loads they can.)

Basically, moving companies do exactly what you’re proposing – they bundle many shipments together and move them in one load. It’s rare for just a single shipment to go across country. Moving companies need to bundle together shipments to make money. You'll probably need at least 1,000 pounds of stuff for them to be interested in your move.

You can also go to U-Ship.com, which is a sort of eBay for moving services. You say how much you need moved and where to, and a variety of transportation providers (not just moving companies) will give you estimates. They’re generally going to a location and need to fill space on their truck.

You could also just go on Craigslist and run an ad or look for ads to track down people who are going across country and have space to spare. There are also self-service options, like ABF, where you load and unload the truck, but someone else does the driving. They will also bundle your shipment with other peoples' shipments.

Finally, you could do the reverse – rent a truck yourself and try to ‘sell’ the extra space you have available.

Whatever you do, check out whoever you work with so that you’re comfortable shipping your things with them. Also, be aware of insurance issues – is the company/person you’re working with insured, licensed, etc? And finally, get it all in writing in case there’s any dispute about timetables, damages, etc. You don’t want to save a few bucks but then face substantial damages – or worse.