The best way I have found to increase push up numbers is to do ladders. Do five sets in a series. Start with 1's. So the workout would be 1, 2, 3, 4, 5, 4, 3, 2, 1. When that becomes easy move to 2's. 2, 4, 6, 8, 10, 8, 6, 4, 2. Then threes. 3, 6, 9, 12, 15, 12, 9, 6, 3. Keep increasing your ladder work out as they become easier. Rest for a short period between steps during the workout. But do not stop. Finish the ladder work out even if you have to do so on your knees. Of course getting propper form down is the first step. When doing push ups look strait ahead, not at the ground, this will keep your butt down. Also focus on contracting your core, it will keep your back strait.
Its always good to work in max sets every once in a while too so you become used to doing so for the prt.
again this is just my opinion, what I havee found to work best for me. Good luck just keep working