Under the Hood
Take the car to your mechanic. Have him check the car from bumper to bumper, list everything that is wrong with the car and how much it will cost to fix. Have him do a compression test and see if it's good. While the spark plugs are out, look to see what story they have to tell. If the porcelain around the center electrode is an even light brown color, that indicates a normal running engine. If it's wet looking and black, this indicates oil burning and is not something you want. Look for any oil leaks around the engine and transmission.
Take a valve cover offThe best way to get a general idea of how well an engine has been maintained is to remove a valve cover. If it's clean, then oil changes were performed fairly regularly. If there's sludge, the car was not well maintained and should be avoided.
Check All The Fluids. Check the fluids and see if they are fresh looking. Transmission fluid should be red, or brown if it's a little older, but never black or burnt smelling. Oil should be a honey to light black color. Power steering fluid should be light brown and should not smell burnt.
Make Sure All The Lights work. Check the head lights, tail lights, brake lights, parking and marker lights. Look for cracked lenses.
Look Under The Car. Go over the brakes with a fine-toothed comb. Look at the calipers and wheel cylinders and see if they are leaking. Look at the rubber hoses and if they have any cracks or cuts, they need to be replaced. See if the steel brake lines, and fuel lines, are heavily rusted. See if the brake pads and shoes are wearing evenly. This is a good sign of a properly operating brake system. Look at the brake fluid; it should be a light honey color. If it's milky or there is a lot of sediment in the reservoir, it needs to be changed.
Look At The Frame. If there is excessive rust or rot, forget about the car. The front end should be tight with no excessive play. CV boots should not be cracked or ripped. If they are, chances are good that there is dirt in the CV joints and they are ready for replacement.
Keep in mind that your son or daughter is going to be driving this car. You want to get them something safe and reliable. If they are going to college this fall, it will bring you peace of mind to know that they will make the trip safely. Don't buy the car if it needs work just because it looks nice or has a nice stereo. Get one that's mechanically sound and buy a nice stereo for it or get it a decent paint job. You have enough to worry about with kids today; their car should not be one of those worries.