In CA, the process is simple. To transfer title, the old owner produces his pink slip (title), and signs it over to you. You sign a piece of it indicating you're taking over ownership which the old owner keeps. He sends his part in. You take your part to the DMV, pay their fees and tax, and the DMV will mail you a new pink slip in a few weeks.
I can't remember how long you have between the time of sale and the time you have to go to the DMV. It's at least a few weeks, maybe 30 days. After that, you pay a fine for filing your change of owner ship late.
More important, you need to be careful about the car you buy. Look it over. At the very least, get its' Vehicle ID number checked through Carfax before you buy anything. You wouldn't believe what people try to pull when they sell used cars.