well I was in the Army and we were tested on pushups, basically we would keep our legs straight and about shoulder width apart (or together) whatever you are comfortable with. Arms slightly further apart then the shoulders again, its about comfort. Then the critical part is keeping your body straight and not bending your back or flexing your hips. Basically keep your head up and looking straight ahead, not towards the ground, then as you go down, all you need is to break your Elbow plane, with slightly touching the ground, just "brushing it" then going up, but not locking your elbows. Just do not round your back or "rest" against the ground.
Best of luck