besides needing correct and rigid posture, including head position, you must have your priorities in check: proper range of motion, elbow orientation, and resistance.
that's too much for me to think about when i'm working out. when i start getting cerebral, i don't focus on the overall goal and i fail on form. that's one reason why they're so hard for me.
one other reason why they're so hard, in general, is because body weight exercises as difficult. you think doing a simple push-up is simple. well, you're wrong.
first and foremost, if someone can't hold their body tightly in a straight line from ankle to ear, they can't do a proper-push up. this alignment should never change throughout the entire exercise. don't push your shoulders up and then later bring your hips up to meet this. that isn't a push-up. that's why you look weird.
secondly, the confusion surrounding the range of motion shouldn't have to be specified, but since it's confusing...here it is. at the top, elbows should be completely extended and shoulder blades protracted. at the bottom, the chest should be in light contact with the floor. all the while, the body should remain straight and rigid.
this range of motion should take precedence over the degree of resistance. if you can't complete a push-up to full depth from your toes, modify your approach and do girlie push-ups from your knees. there's absolutely no shame in doing them this way.
though difficult on the ego to master push-ups, the benefits are worth the embarrassment. nobody loads weights to bench press only half way down because it's too heavy. they start with a weight they can move through the entire range of motion and build up from there. the push-up should be viewed the same.
keep your upper arms within about 45 degrees from the side of your body. this will allow the shoulder to move through that full range of motion more easily and naturally. moving the hands wider and bringing the elbows farther from the sides will usually make push-ups easier for people but it also limits depth and starts tearing up the shoulders pretty quickly.
when performed well, a push-up doesn't draw attention. it's not a flashy feat of athleticism. but how a person performs a push-up is indicative of their athletic foundation and their commitment to excellence and performance.
put a little attention and effort into the simplest things and it will pay returns in the more complicated and interesting ones.
eat clean. live lean. live better. live longer.