It all depends. Body builders tend to not be healthy eaters, they just take in tons of protein and calories. But if you are trying to get super thin and cut then you are going to need a good diet. But no matter what your diet is if you burn more calories than you take in you're going to lose weight -- it's physics. Also, any daily physical activity is going to benefit you. Just start doing 100 push-ups a day and rest when needed, and you're going to see that you will get stronger. Whereas, doing 20 in a row might be hard at first, in a few weeks 20 won't be as hard. Then in a few months 20 won't feel like you're even doing much and it will push you to do more since 20 is easy. And it's the same with any exercise.
One thing to remember if you really want to get stronger is to push until failure. What I mean is say your goal is 100 Push-ups. Your first set just do something easy. Maybe 5, or 10. But don't push until you're unable to do anymore. This will warm your muscles up. Then the sets you do after that push until you can't do anymore, or very close to that point. Then rest a bit. And the next set do the same. If you are always pushing until failure or close to failure you are going to progress in strength and stamina.
Also remember to rest. When you are felling sore and tired take a day off. If the next day you still feel tired and sore take that day off as well. This is actually the time when your muscles are growing and developing. The way you develop muscles is you tear them down, and allow them to rebuild. After you allow your body to rest that first day you start working out again is awesome because you are going to see how much stronger you've become.