I'm not sure if you've already been trying this, but try say 4 sets of 10-15 with 30 seconds rest between sets. Increase the number of reps each week, or if possible, increase the number of reps by 1 each day. I found this helped me a lot when I first started.
When you get up to say 30 reps for each set, add another set.
As they say, practive makes perfect, so just keep banging them out
I agree with Ayrey on this one. Press-ups and more of 'em.
The main sets of muscles involved in press-ups are the triceps (at the back of the upper arm) and the pectoral (chest) muscles. You can vary the stress on both by rearranging your hands on the floor. With your hands pointing inward, you bring the pectoral muscles more into play, while with your hands in the same direction as your body, the triceps take over most of the work.
In addition to press-ups, you need to increase the strength of your triceps with deep dips, either on bars or between two chairs.
If you're reeeally pushed, you can drop your arrse two inches towards the floor; this brings a further part of the triceps into action and should be good for about five more reps. However, it's likely that you'll get pulled up on this by a PTI.
Serious head on... It's not your arms which give way, it's your mind.
Being able to do los of reps is great, as it is a good measure of your muscular endurance. To increase muscular endurance, you obviously have to try and do more reps. Except what people forget is that the longer you can keep your muscles working, the greater the impact on endurance.
Instead of 'letting your arms give way' when you get to that point where you just can't do another rep, try locking out your arms and resting for a 10 seconds (you will actually still be using your muscles to hold yourself up). Then try doing a few more. Even if you can only do one more, and you really struggle to get all the way back up, it's still doing you a huge amount of good. Then hold yourself in position for as long as you can.
Stop counting how many pressups you are doing. Instead, do as many pressups as it takes to get tired, and then do what I've described above. Instead count how long you can hold yourself up for when your muscles are screaming at you. If you do this just once everyday you should find that within a week you have doubled the number of pressups you can actually do. And you'll achieve the bonus factor of teaching yourself a bit of mental toughness as well, which will come in very handy when you start at ATR!
Stop trying to do lots of press ups for a start!!
Sounds daft but try this it will build muscle faster and then you will be able to do more pres ups.
Get in to the press up position and take 3 seconds to get chest to the ground and 2 seconds to get back up. You have to be rigid with the timings. Dont stop at a given number stop when you cant do any more. Have a break of atleast 1 min to allow the glycegen and oxygen to build up in your muscles. and repeat again do 3 sets reping to failure. do this every second day and you will have amazing results in no time. Once you have done this for 2 weeks have burst and see how many you can do you will probably be up at around 40+ if you have stuck rigidly to what I have said.
Some excellent advice on here, especially from ayre and bits. I would just add two things. in addition to the press up workouts you should do a bench press workout once a week. 5 sets of 5 reps with enough weight to be very hard but do not approach failure, add weight when you can. this will give you the power to do press ups fast, easy and controlled. vital if you want to achieve big numbers
Also it is very important to measure progress, A chart pinned up on a prominent wall is ideal, and dont hide it away let others see it! Feed on other peoples input, if it is negative use it to strengthen your resolve, if it is positive
Heard some good advice somewhere on arrse about doing the press-up movement slowly - 3secs going down, 2secs coming back up to fatigue then resting for a min or two then repeating. Been doing this for a couple of weeks and it works a treat!