When you are about to buy a used car, you should carefully look at the car inside and out. The first thing to look at is the oil and other liquids in the engine. Look at the color of the oil. If the oil is pretty dark or black, that is a sign that it needs to be changed. Look at the valve covers to see if there is oil residue around the edges of the covers.
If so, it is time for new valve cover gaskets to be installed. Look at the radiator fluid to see if the antifreeze is good. If it is discolored, it will need to be changed along with flushing of the cooling system. If the odometer is mechanical, look at the far left odometer wheel and see if there are any scratch marks. If scratch marks are present, it is possible that the mileage may have been tampered with.
Make sure that the same wheel is centered. If it is not lined up with the rest of the odometer wheels, that can be another sign of tampering. Fingerprints on the dial can indicate tampering. Look at the tires and see what type of wear is shown. An indication of poor alignment is when the front tire wear is more on the left or right side of the tire tread.
The way to test the alignment while driving is to drive at 30 and 60 miles per hour. If the car pulls to the right or left, the alignment can be out. This is most important on the front wheels. Look at the transmission fluid to see if it is full. This is done while engine is running.
Put the car in reverse and all the other gears. Put back in park and check the transmission dipstick. Look at the color of the fluid. If the color is a light pink/red color, it is usually good. If the color of the fluid is a dark red, it should be replaced along with the filter.
Look for any rust under the car along the frame. Look for rust on the exhaust. Look for rust inside the car under the carpets to see if the car is a flood car. Checking under the seats is also a good place to check for rust. That is a big indicator of a flood car. Last thing is to get a vehicle history report.
I am an auto technician. This is from my own expertise.