Accept only CASH for the car. Make sure you see the person's license with address etc so you can make sure the DMV papers are correct. Make a copy for yourself and get a receipt for the sale of the car.. signed by both parties.
VERY IMPORTANT STUFF! Or better yet, go to the DMV with the buyer and transfer the title in person.
We sold one car and the buyer just gave us a bad feeling, he kept trying to talk down the price, or talk us into a trade (he has a few cars for sale) was a real "wheeler dealer" type, but he wife really wanted our car and we didn't budge. He showed up with a check, and we refused it... took him four days to come back with cash (we almost sold it to someone else cuz he didn't return our calls) so we drew up purchase agreements and recorded his Driver's License number and info, signed them, etc. - he was in "too much of a hurry" to go to the DMV with us (big warning flag, it's only 5 minutes away) so we let it go, were just glad to be done with it. Sure enough, 8 months later we got a notice our license tabs were due, the guy had never transferred the title. Luckily we had all the info on the purchase agreement/receipt we had him sign and we had to file some additional paperwork with the State to transfer the title. (We tried to call the guy but never returned our calls - unfortunately for him he then owed a penalty of several hundred dollars for not filing the transfer within the allotted time) luckily there were no accidents or tickets during those 8 months or it could have gotten very complicated.
In our State, the buyer has to pay full sales tax when they transfer the title so often they prefer not to go with the seller as they report a lower purchase price than what they actually paid, but living so close to a DMV office we pretty much insist on it after that hassle.
Oh, and we've tried newspaper and online ad's, but we've had the best luck having the car professionally detailed/cleaned, and parking it on a relatively busy street with a "For-sale" sign in the window during the day.