I've done pushups in a haphazard manner for years, reaching an unsustained peak of about 30 in a continuous set. But I've recently gotten some motivation and a structured approach using an Andriod app: 100 Pushups. With it, I'm doing an ever increasing number of pushups in just 10 minutes every other day.
My current level - over 80 pushups in a noncontinuous set. Its not easy, it takes all I've got, but its working; I feel stronger in my chest and abdomen already (pushups do more than work triceps.) If you're interested, this app can take you from no pushups, to many, in just 6 weeks. Give it a try.