In addition to tlhIngan's answer;
Get the VIN number of the car you're looking at, and get the vehicle history report. Compare it with anything the owner tells you.
Find out how long the previous owner has had the car - longer is better, and if they've owned it less than 6 months, be even more thorough on your checks - they may be trying to offload a lemon.
Look at the local area that your buying the car from, and the people you're buying from. if you don't feel comfortable, walk away. Honest people sell honest cars.
If you don't feel confident checking the mechanicals, ask for an inspection to be made. At least, get an MOT / Safety Inspection done before buying.