Back before I bothered to try to work out, I was lucky to make it to ten push-ups within a minute. I maxed myself out on push-ups (among other things) hitting about 15 before I just couldn't and I had the most ungodly muscle aches the next day. Did my best again, this time a mere ten, then the next day, being in so much pain, waited a day. My muscles didn't hurt so much, so I tried it again.
Boom! 20 push ups in less than thirty seconds. I think part of it is muscle conditioning, but if you're an inactive person, don't be too horribly worried about a dismal amount. It'll go up very quickly.
After that point, I increased how many push-ups I did by five each week. So, as for an answer, I'll echo a person above me: do as many as you can, then when that becomes less a chore, increase it.