Instead of sets of, say, 10—which you can't do yet—do a set of just one or two reps. Then rest (or do another exercise), and come back for another push-up or two. You may want to do more sets ...

I participated in the 22 push-ups in 22 Days challenge #22PushupChallenge to raised awareness for Veterans suffering post-traumatic stress disorder (PTSD) and in particular the absurd suicide rate ...