My neighbor sells used cars (mostly upper end Mercedes and BMW). If I see him in the next day or so I'll ask about taxes. He's Iranian and I suspect he exports some go to Iran. For what few cars I've bought from private sellers, I don't remember paying taxes.
Even though this is going to be a one-shot transaction, I would strongly recommend joining the American Automobile Association. (google AAA for the local branch name where you'll be buying the car. Here in LA its called the Automobile Club of Southern California.) It'll cost about $65 to join. It's possible that this could be the best $65 you've ever spent. The AAA can do all the paperwork; change title, registration, provide a CA license plate and collect the plate fees, etc. They will also inspect the car as required by the California Department of Motor Vehicles. If you want to smog the car, you will have to have the car smogged yourself.
For export, you probably only have to do the paperwork to get legal title. You can also get temporary license plates that allow you to drive the car for a brief period.
The reason for going to the AAA instead of the DMV (Department of Motor Vehicles) is that the AAA employees are helpful, courteous, and intelligent. The DMV employees are government workers, often uninterested, and can sometimes take delight in using the rules and regulations to make things difficult for you. Plus long waiting lines at the DMV. AAA
Fees:
Fees for title transfer and temporary license plate (if you want it) are pretty minimal. I would guess you will have to pay a sales tax if you buy from a dealer, the tax is about 8 1/2 percent of the purchase price. Residents have to pay sales tax and even though exported,, I'd image you'd also. If you buy from a private person you have to pay a use tax which is 8 1/2 percent of the purchase price. When buying from a private person you can understate the purchase price and save on taxes. If your stated price is suspected as being too low, you may be challenged.
If you get a permanent registration and the accompanying license plate, the fee is based on the value of the car. The registration for my C6 was about $800. For my 68, it's maybe something like $60 (?). For old cars, the registration will be the minimum regardless of the amount you paid for it. Also as for smog, there's no smog test for cars made in 1975 and before. If you're getting an old car, it might make exporting more convenient just go ahead and register and get CA tags. Perhaps it might be easier with customs to have the car fully registered and licensed in the name of the buyer - I don't know.
