Whenever I've sold a car to a private party:
1. take money
2. *take your plates off the car*
3. sign over title
4. wave bye-bye
5. call your insurance company and remove car from policy
6. notify DMV, turn in plates and get refund for remaining value of
registration
The buyer should come with temporary tags in order to drive away.
Alternatively, if you are a nice guy, you and a buddy can drop the car
off in the buyer's driveway, do the transaction and get a lift home in
your buddy's car. You are not responsible for waiting at the DMV for
the buyer to get new plates. In some states you are responsible for
selling an inspected car.

When selling my '93 Honda Accord is it to both parties advantage to go
to the DMV together to transfer title and finalize the deal
(California)? Someone wanted to buy the car off me last night after
driving it around the block. He had the money but I didn't feel
comfortable with his haste. I have a feeling  something may happen to
the car before he gets around to going to the DMV and it may be my
problem.  Should I insist on going to the DMV together?