Good luck...I did this with my wife's Escape a few years back, and it's not worth the extra $$ I got over the dealer's low-ball trade. I'll NEVER try and sell a car myself again. Well...maybe not never, but not unless the extra profit is in the thousands...
-eoMMan's point is good. Make them sign a bill of sale indicating the car, date, money, and note that it's binding, and not returnable. A lot of whackos will buy it, go drive it for 3 weeks, then find something they like better or something and want their money back. That one line is usually all it takes to make them realize that it's theirs once they leave your property.
-Take your plates. If they don't have plates to get it to the DMV, go with them. Don't let them drive away with your plates (seems obvious, but not everyone knows that)
-If you're using Craigslist, be prepared for the whackos. People will point out EVERY SINGLE DETAIL that is wrong with your car. "You've got a little oil residue on your drain plug." "You've got some minor rust on your exhaust." "I think your wiper blades need replaced." "You're going to need new tires in 2,000 miles." I got SO sick of it. I eventually just started using the canned response, "OK. It's a used car. Selling it as-is." So many people wanted me to fix things before they'd make an offer. NEVER do that. 90% of the time, you'll fix it, and they will be long gone.
-Nobody who says, "I'll be back" ever comes back, so don't hold it for them.
-Be prepared to get 80% complete low-ball offers....Not like 10-15% off...I'm talking 25-50% less than you're asking. I actually laughed at a few of them.
-Re. letting people drive them, I based it on what kind of car they drove to my place. If they drove up in a decent vehicle and left it, I let some folks just go drive on their own after I photocopied their DL. Others, I rode along.
-If someone wanted to take it to a mechanic on their dollar, I'm fine with that.
-Again, good luck. I had ours posted for 3 months. I saw an average of a potential buyer every week or so. 50% looked, liked it and never made an offer. 25% made super low-ball offers that weren't even worth negotiating. Some just came to criticize the car, expecting something "new" and then left when I told them it was a "used" car sold as-is. I had one kid who agreed on a price, shook hands, and headed off to the bank to get a cashier's check. About 4 hours later, after I spent time drafting a bill of sale and getting the car ready for sale, he called and said he'd changed his mind. I let him know that in the future, when a man shakes hands, a man honors his word. Finally ended up selling the car to my wife's cousin, and even he wasn't happy when the AC broke after he drove it from NJ to Colorado.