The push-up is one of the best exercises for you. You can do push-ups anywhere, wearing anything. Push-ups can be modified to make them easier or harder. You can change your hard positioning to work different muscles more. You can also wear a weight vest which increases resistance.
Muscle groups involved:
1)Arms
2)Back
3)Chest
4)Abs/Core*
5)Shoulders
*I don't know if any of you have heard of the plank. It is a great core exercise and it is quite effective. I have recently stopped doing the plank because I am able to do it for about 5 minutes and quite frankly it is really boring. If you are able to do a substantial amount of push-ups you can simply substitute more push-ups for the plank.
These are the muscles that you use when you do push-ups.
1) Knee Push-up (modified for beginners)
2) Regular push-up
3) Push-up plus
3) Incline push-up
4) Diamond push-up
6) Clap/Jump push-up
7) Alternating jump push-up
8) Resistance push ups*
9) One handed push-up
*You can where a weight vest or simply put weights on your back. Make sure the weights are distributed well enough so you do not feel pain in your back or core muscles. If it is painful (more than sore) stop doing this immediately and stick with regular push-ups or one of the modifications.
My Personal Experience:
I used to not be able to do many push-ups. When I started doing them seriously (at least 4 times a week), I could do about 15 and then I would have to stop. I'm talking actual push-ups, so body straight, nose to the ground, and all the way back up. If you do them incorrectly, or do not go all out, you are only cheating yourself. If you work hard and actually do push-ups often, you will see serious results and improvement. I was able to do about 60 straight after only a couple months. The push-ups will become easier, so you will be able to do more reps, or you can try some of the push-ups listed above.