I've done this two times, both with people from online postings, but they were within groups my wife was a part of, so we could trust they were actual people. I posted details about the car with a price. Anyone who wanted to barter or make an offer, I ignored. From those offering the asking price, I just picked one, met with them, had them drive it around, and signed it over.
Our state's DoL website has a form to fill out. I recall it being pretty straightforward, though there is a small window of time to complete it.