One method is doing sets of 10 reps (or whatever number of pushups you can do in a row right now) and gradually reduce the time between sets. For instance, you

One method is doing sets of 10 reps (or whatever number of pushups you can do in a row right now) and gradually reduce the time between sets. For instance, you start resting 60 seconds between sets. After a week, you rest 40 seconds between sets. And so on and so forth. After a few of months you should be able to do 40 pushups in a row.