1. Know your price range and keep to it. I generally use Cars.com, Craigslist, call on cars I see driving around town, or in the paper.
2. Get your money ready/financing in place ahead of time. Having this ready will help you in negotiating a price for the car. Motivated sellers will generally take an even ower offer if they know you have the cash to buy the car quickly.
3. Find vehicles already priced at or below KBB.com private party pricing. Also check average pricing on Cars.com, because supply and demand drives pricing more than KBB. Look for "motivated seller", "need to sell", "extra car", "divorce", "moving" etc.
4. Ask lots of questions: who, what, where, when, why, how long, miles, how does it run, does it need any work, is the title free and clear, is it salvage, etc. You can get the VIN (vehicle identification number) and run a CarFax as well.
5. Always meet in a well lit public place. Do not ever meet at your house, preferrably a grocery store or bank where there are cameras in use, and ladies- make sure you bring someone with you. ( I never test drive in the vehicle with the person selling it alone.)
6. Either bring a friend who is mechanically inclined, or arrange for the vehicle to be checked out at a local auto shop you trust. Understand this is a used car and it will not be perfect- you are mainly looking for a sound engine and to be alerted to any major issues. There are no take backs when buying a used car. Just know what you are getting into, and be aware that it may be running perfect the day you buy it and something could go wrong the very next day- that is now your responsibility.
7. When you are ready to buy, meet at the seller's bank, and have the banker verify the cash, or cashiers check there. (Cashiers checks are best made out to you if you get one from your credit union, etc., then cashed at your bank, and handle the rest in cash at their bank.) This is neat and clean and you have receipt of the transaction.
Also when you are at the bank you can have the title notarized at the same time, since you will want the title in hand as you hand over the money.
The title is the bill of sale, however, you may want to print a bill of sale up from Cars.com or from your local DMV, since you may need the DMV specific one to register the vehicle in your name. Check with your DMV also to see if current plates transfer (here in AZ we keep our own plates).
Those are just used vehicle buying tips that come to mind. I have learned these myself and I know they have helped some of my friends, maybe they can help you too!