Watch one of my tennis players use a "jump-stretch" band in the power rack to help him with his push-ups. All you do is loop the band in the safety bars. Each workout we decrease the band tension a little bit until he can start banging out push-ups on his own!
Notice he is working on keeping his elbows in to get lots of tricep involvement and to not place all the pressure on his shoulder. Notice he goes all the way down and all the way up as well! No half-reps allowed.