If you are living in California for an extended period of time, you must register your car with the Department of Motor Vehicles (DMV). While crossing the border, you can ask U.S. customs for the paperwork which you will need for registration. If you forget, it may be possible to get the paperwork from customs at SFO airport. The DMV might also ask for paperwork specifying emission standards for the vehicle: it may be possible to acquire this information from the car company. It's important to check that your vehicle will be acceptable to the U.S. Department of Transportation: differences like seat belt configuration can prevent you from registering. Don't rely on a border guard to check for you!
If you're coming to the US as a tourist for 1 year or less, you may be able to buy "Territory Z" insurance in Canada and keep your car insured and registered in Canada.