Well if your having problems doing full push ups, that just means you need an smaller start. Instead of doing the 'normal' push up where you pivot on your toes, your going to want to try pivoting on your knees. (You'll learn in physics how the verticle force needed to push yourself up is reduced when the angle between your body and the floor increases.) Start out doing those types of pushups until you get the strenght to do the full pushups. Also if you have a bench that's elevated (about a foot or so) you can also use that for pushups. Keep your feet on the ground, put your hands on the bench, and do a push up.
Don't forget to stretch your triceps (back of the arm) and chest.