A proper push-up takes you all the way down to the ground -- but it's easy to cheat by only going partway down. To be sure you're getting the full challenge and benefit out of each rep, pick up your hands every time your chest hits the floor.
Extend your arms out to the side, as shown in the video, and you'll have no doubt about whether you've actually gone deep enough. This also gives you a second of rest, so that when you push back up, it's like a fresh first rep all over again -- no more pumping up and down with bad form.
If you're used to doing shallower push-ups, this technique might be difficult at first. But rest assured that you're doing better push-ups this way, even if you can't bang out quite as many reps.