there are 2 ways to increase the number of pushups you can do.
1. Build strength
2. Lose fat (dead weight)
1. Do bench press. Allow 3 days to 1 week between workouts (you will have to find out which is best for you). The weights should be so heavy that you can only do about 7 presses. Do 3 sets of these. Eat a lot of protein (at least 100 grams per day...i recommend going to GNC and buying a protein shake).
2. Lose fat by watching what you eat. You need to eat protein to build your strength, but don't eat junk food. Drink a lot of water.
In about 2 months, you will double the number of pushups you can do. I know because this is what I did this summer