There is a correct way to do a push up and I decided to say that in my blog because I so often see the incorrect way.
Whether you choose to do a full push up - straight leg weight on balls of feet or toes or a bent leg - weight on your knees, the goal is the same. Push ups require the use of several muscle groups, including your arms and core. The main groups that are worked are the chest and back.
Hands are usually somewhat wider than shoulders and the torso should be held straight by using your core or abdominal muscles. You slowly release your weight into your hands and go down to about an inch or two from the ground as a whole straight unit. The chest is the focus and should lead but more or less you stay in a straight line. The bottom of the pushup is when the chest and body is hovering an inch or so from the ground and then you push the weight back up so that your elbows are no longer bent.
Incorrect: having your stomach or hips closer to the ground than your chest. Ironically, the majority of men that I have seen doing pushups, do so with a swayed back.