How do you train to max pushups on an APFT?

I like to do 30:30s. 30 seconds of pushup 30 seconds rest. Do as many pushups as you can in those 30 seconds but the goal is 20 because if you do 20 for each 30 seconds in a 2 minute test you did 80 push ups. Even in the test I do 20, take a rest position for a few seconds and then resume pushups. Once you can hit 20 pushups in 4 sets of 30:30s then you add more sets to make it more challenging.

Alright, here's how you do it. You can max it today. First, find an NCO that doesn't like you to show you what a "correct push-up standard" is with your body structure. This person will be more than happy to make you do it correctly. Now, using the correct technique, perform and count your push-ups backward from 72 to 1 as fast as you can go. Don't forget to breathe. Do this every night, starting 3 weeks before the test. It will be a piece of cake on game day. The brain loves to perform backward, but hates forward for some reason. Did it and taught it for years. Good luck!

Weight training. Wear a weighted vest or even an IBA or something like that and you'll see a drastic improvement.