Before you start negotiating, make a list of as many of the arguments for lowering the price as you can. It is best to start by researching the model you would like to buy. Check typical faults, how many miles they are and what costs they cause, so you can get a discount on future repair costs once you've had a chance to check the car's condition and check the service book. Also, check out similar offers - this may be the easiest way to convince the seller. Chances are, the seller will decide it's better to give a discount and sell the car than to let you move on to a competitor.
At the point of purchase, ask for a test drive and make sure you can examine the car in detail. There will always be some flaws, minor or major, that can be used to get a discount.