To get composition right you need to think about a few things.
Below are 2 very simple photos, nothing complex about these at all (other than the fact she was darting around very quickly!) However, in my opinion, one looks far more pleasing to the eye than the other. Why?
1) In the left photo the horizon is nice and straight. Some images can look quite good taken on a tilt but not for a photo like this. I think it can work with objects but for me personally, a tilt is really distracting and unnecessary when taking photos of people.
2) In the left photo she is not walking straight towards the camera but to a slight angle. The photo on the right, she is clearly walking at quite a pace and it feels a bit squashed for space! You don’t always have to be directly in front of your subject.
3) In the left photo, the background is nice and clear and the tree to the left helps frame the image in a way. However, in the right photo there is a tree directly behind her, giving the image an unbalanced feel and distracting from the subject. If the tree was any more narrow, it would look like it was growing out of her head!
4) Finally in the left photo the proportion of sky and ground above/below the horizon is quite nice. About 2/3rds ground which works as it emphasises the autumn leaves (the mum wanted a really autumn feeling shoot). If the ground was plain grass or concrete, I would have changed the balance. However, in the photo on the right there is too much ground and its become unbalanced, especially considering the tree.
Of course, some of things you may be saying can be changed in photo editing software afterwards, but nothing beats getting it right in-camera. These tips are about photography!