Now I haven't read any of the replies to this post, so some of this may have already been said.
I just completed OCS in May and regularly complete the max of 87 pushups. I was also the PT Body for my class in which everyone except 1 person passed the out PRT. I worked nightly with several individuals on their pushup form and helped them pass. I'm also an avid weight lifter, so I consider my advice as sound.
Start by counting backwards. Your goal should be 87 I'm guessing, since that is the max. So start off at 87 each time and count backwards. You'll be surprised how much easier it is. As you improve in numbers, you get closer and closer to 1.
Since you're working now on trying to build your number up, don't try doing as many as you can as fast as you can. You only do that when you're actually doing the test for real. Work on technique and strength building.
Keep good form when you do each one. Remember nobody cares if you can do them all or not except yourself, so don't lie to or cheat yourself. Proper form is just like they say: when you're in the pushup position, your heels, butt, backn and head are all aligned in a straight line. No dippng or raising your butt allowed. It's best to have hands shoulder width appart, not spred way out. You want them closer together. This way seems harder to do at first, but once you get used to doing them, you can do a whole lot more in a shorter amount of time then with your arms out.
The motion is simple, all the way down till your elbows bend 90 degrees, then all the way back up and keep your back, head, butt, and legs straight and aligned.
If you have at least a month to improve and can do pushups daily or at least 5 days a week try this: Strap a seabag, or backpack with books in it to your back and do 4 sets of as many reps you can do. Do this for 1 week, then cut the weight of books in half and do that for the next week. The last 2 weeks dont use any books as you dont want to continue breaking down your muscles and you want to build repetitions not strength.
If you are like a bunch of us, you have trouble holding the pushup position for the whole 2 mins probably because you're lower back is weak. So do this: get in the pushup position and stay there in the up position for 1 min (longer if that's easy for you to start) Dont do any pushups, just sit there in the up position. This will build those muscles you use to hold your form. Do that for say 3 sets. You can combine things by doing a set of pushups, then once you cant do anymore, hold yourself up for another min. Once you can start fresh and hold yourself up for 3mins straight, you'll be strong enough to do pushups for 2 mins w/out bending or arching your back while doing the pushups.
Hope this helped out for you!
Matt