Some of these might be obvious, but reminders never hurt.
It's tricky going out to buy a used car. The obvious piece of advice is to not be a dumbass, but that doesn't always work. In the wake of that beautiful 1968 Charger your mind floods with all the ridiculous things you're going to do with it, and logic goes Mach 3 out the window. Fortunately there are some good ways to make sure you don't get screwed. This isn't the end all and be all checklist for buying a used car, but following each one of these steps will certainly help ensure you don't get screwed over.
Make sure it has a title. There are two reasons to do this, and the first is because you don't want to deal with an obscene amount of DMV paperwork, especially if you live in California. Because of smog laws, not having the title is a complete nightmare to deal with when at the DMV. Make sure it has a clean title as well. There are a few ways to get a salvage title. One is if the car has been damaged somehow and the cost to repair the damage is more than the car is worth. Chances are you don't know the guy selling you that Charger on Craigslist from Adam so he (or she), might lie about how it got the salvage title. Either way, finding out the hard way later that the car has frame damage is not worth the risk.
The thing to remember about mileage is parts on the car begin to fail after a while. Be sure to do your math. The average American drives approximately 13,476 miles per year (however insurance companies like AAA use an average of 12,000 miles per year to base rates on). Regardless, a car from 1996, which is 20 years old, is "allowed" to have approximately 270,000 miles. However just because the mileage is supposed to be 270,000 doesn't mean it's necessarily low. Now if a 1996 car has closer to 130,000 miles, that could be considered low mileage. Just be aware of the car's weak points, which brings us to the next tip.
Do your research. Check the recall history, because if you get this car from 1996 with a bad thermostat housing (like with E36 BMWs) without checking, suddenly you're driving down a popular street and coolant starts bursting out from under the hood. It happens. Don't forget to check with the dealerships before you fix something that was recalled. If they look up the car's VIN and see that the recalled part wasn't fixed, they should do it at no charge. Sometimes parts fail on cars that aren't part of a recall though, and depending on what the defective part is it might be a deal-breaker. If it's something like an A/C switch then that's probably OK, but a timing chain problem is something you should probably stay away from.
Check everything, in every sense of the word. Look for rust, cracked dust boots, leaks, run your fingers along the brake rotors to check for a lip, check the pads. Look in the trunk for corrosion, look in the engine bay for hoses with holes or corrosion, make sure the lights work, avoid things like aftermarket alarms (unless you get it installed yourself). Check bushings, tire tread, shocks, and everything else. Get service receipts if the seller still has them. Check things like wheel studs (because some might not be there), check the wheels for chips or other damage. Be sure to smell the interior of the car. It sounds weird but if there's a suspect smell coming from inside, it could be a red flag.
Of course you should drive the car. If the seller doesn't want to give you a test drive, it's a deal-breaker. A big reason they wouldn't let you drive their car is to hide something from you. Sometimes what a seller will do is drive the car with you inside, and with that you get at least some sense of how the car behaves. But you should insist to drive it yourself and walk away if the seller refuses. While driving repeat tip #4: Check everything. Alignment, acceleration, braking, steering, visibility, and be aware of how the tires are behaving. Sometimes if the alignment is bad the tires will get uneven tread and that will reflect in how the car behaves.