Push-ups are one of the oldest exercises known to mankind. You don’t have to be a push-up champion to do push-ups. Many people start out with their knees on the ground to build strength. With your knees off (or even on) the ground, place your hands at shoulder alignment and then come down to the ground slowly.
For maximum results, make sure that you come down almost all the way to the ground. Many people do not go all the way to the ground, which is why they won’t see great results. Do your push-ups the same amount of time that you do your triceps dips and you should see your strength increase to the point of being able to do push-ups the proper way.