Firstly, typically you won't deal with the trucking company itself. Usually when you are talking to a transport company, you are really just talking to a broker.
Here is how it works:
The broker gives you a price for the job. Part of the price is his/her broker fee, the rest is for the trucking company. You want to find out exactly what the broker fee is, and find a broker with a reasonable fee.
Now, the broker can quote you whatever price they want (and you will get a wide range of prices - some really low), and you have to be really REALLY careful about this part. All the brokers are really doing is taking the part of quoted price left over after their broker's fee, and posting it up on a computer system that truckers monitor.
If a truck has a free spot, is passing close to the start and end points, and the price is high enough, they will take the job.
IMPORTANT: if the broker gives you a really attractive low price, your car will NEVER get moved. The price will be too low, and no trucker will take the job because they won't make any money on the deal.
So, there is a tricky balancing act going on. You want to offer enough for the job to be attractive to the trucking companies, but not so high that you are paying too much. Time is also a factor. If you want it to happen quickly, you either need to be lucky, or pay a bit more to make the job more attractive. If time isn't a factor, then a lower price may eventually get the job done because the right trucker just happens to be passing through and the start/end points line up exactly with his current deliveries. This is where a good broker is helpful. They will know where that line is and help you pay the right price for the time frame you want the car moved in. Price, obviously, also totally depends on the distance, amount of truck traffic through the start/end points, etc.
I'm currently have a 66 coupe shipped, and what Skitzo said is very true. I initially went with the low bidder, and they couldn't get a trucker to do the job for the money offered. I canceled that contract and went with Assurance Auto Transports and they found a trucker is less than 24 hours. The final cost was $650 which included $125 going to the broker.
I'm rust belter who drives cars that are super clean low mileage, zero rust cars about 8-10 years old when I buy them. In 6 years I've bought 5 cars in the Fort Worth area. Each has been transported to our home in southeast Wisconsin by D.A.S. No problem on any of the 5. They were recommended, I got no other bids.
One other bit to add to Skitso's....
These trucking companies have terminals that they deliver/pick up at.
You'll be offered 4 different prices,
"terminal-to-terminal" (least expensive, but the seller has to get the car there, and you have to get it at the terminal near you)
and "door-to-door" (most expensive, but the easiest)
I had my dads '68 Coupe shipped from Anaheim, to Mass. in NOV. 2007.
I also used DAS, it was $1150+-
I used the door-to-door, DAS delivered to a local shop that they contract with to deliver cars. This is due to the fact that some of the larger carriers can't navigate small roads, so the car got put on a small flat-bed at the local shop, that brought it to the house.
Some larger trucking companies may switch your car between trucks that have set routes. If you have a really nice car, you might want to ask about that. The more load/unload sequences the more chances of something bad happening. I'm not sure if this is a real issue or not, but I didn't want to use a company that would switch because although my car was a roller, it wasn't a breaker (no breaks!).
I've shipped cars half a dozen times around various parts of the country. All the above it spot on advice. You can also pay extra to have your car on the top if you are worried about another car dripping onto your car on the bottom.
If you can do a terminal to terminal with DAS you probably won't find a better deal by a reputable company. They tend to be more expensive for door to door than going through a broker. I've done all the combinations listed above with no issues.
A couple other tips. Once the broker puts you in contact with the driver (more likely the driver will call you), it is completely between you and the driver about exact time for pick-up and delivery. I've worked out some good deals with them to meet their schedule and I'm always there for load and unload. The more you talk to the driver the more likely they are to treat your car good. I've never met a bad driver...that goes for moving company drivers as well.
Use the info provided to make sure your company is bonded and insured.
If you can spare the time and don't think the car can drive that far, you can always rent a u-haul truck with a full car trailer and tow it yourself. It will probably be cheaper and certainly no more expensive than paying someone, but you'll have the peace of mind. Even with a one-way plane ticket between LA and Seattle you'll probably at least break even. I've done this as well.
"uShip is an online shipping marketplace that connects people with customer-reviewed transport companies that can move hard-to-ship items such as cars. Transporters place competing bids to win a customer's business, which brings down delivery costs and makes shipping more affordable and efficient."
I used uShip to move my car from California to Iowa back in 2008. I just got done using them again to ship it back to California. It was really easy to use and I had about 18 bids for our van and 12 for our mustang. I liked that you could see the feedback of the companies bidding on your shipment.
Thanks everyone for the great advice. I have two cars and not sure I want to make the drive twice. I had the stang shipped to LA a decade ago and it worked out well. Can't recall who I used though. But now I have some great referrals.