there are soooooo many thinngs to check before buying a used car. im not sure if anyone can explain it to u this way. because even the most experienced people over look some issues in a car.
well, generally speaking. just check the body first, look for rust, paint not matching, look in the engine bay and under the bonnet if u can find any welded spots. see if the doors etc are out of allignment etc
then go inside the car. look for irregularities on the exterior. any scratches, broken parts etc.
take a test drive, turn the sound system and a/c fan off and try to listen if suspension gives any sort of sound. then revv the engine and hear if theres any rattling or abnormal sound. then turn on the fan and check the a/c. all the buttons on the interior etc.
and after all, check the documents of the car.that is the most important aspect of a car. if the booklet is stamped as duplicate, know that the car should be bought around 60-90k below its market value according to condition. this doesnt makes any sense but thats how our market work.