The push-up is one of the best upper body exercises you can do. There are a tremendous number of variations that target different muscle groups and that range in difficulty, and you can perform this exercise anywhere, anytime. Unfortunately, many people struggle to execute the push-up correctly, and as a result, do not reap the benefits of this great exercise.
I find that when many people perform the push-up, when they reach the bottom position and are about to push back up, they disengage their core (basically all of the muscles that stabilize the pelvis, spine, and scapulae). The end result is that their back hyperextends, hips and neck collapse, and this loss of spinal stiffness/full body rigidity prevents them from performing the exercise properly, and from being able to generate significantly more power with their upper body.
While I like to reset before the start of each rep by setting the body so it's in a straight line from the head to heels, actively tucking the rib cage towards the pelvis, taking a deep breath in (360 degrees of air around the spine), bracing the core, and squeezing the glutes, I also find that when you approach the bottom position and are about to push back up, it is very helpful to imagine that you are about to get punched in the stomach. This will remind you to keep your core braced/glutes engaged, and will prevent the rapid deterioration in form from occurring.
If you struggle to maintain proper form during your push-ups, give these tips a try. Here are 4 different push-ups that range in difficulty. I am able to do these largely because I am doing what I described above.