I do like this shot, but know that it is far away from being as good as it could be.  I am terrible at composition, what do I need to change to make it better? Please bear in mind that is was taken with a compact (seriously considering a D40).


Bigger

Move slightly to the right and frame the face with the flowers, rather than cover it.  Use the rule of thirds.  Experiment too with having only the face in focus (focussed on the eyes).

Nice though.

Eagle has it exactly, in this case it depends on what you are representing,  what you want to be the main subject, if you were after the flower then its great, the girl then its not so good. Moving a little to the right would have solved the issue as already said but this could have put the flowers out of focus.

If you want both in focus then you need to step down the aperature (A few compacts have aperature priority or a depth of field program) or take two photographs, one with the flower in focus and the other with the girl, then combine the results in an editing program. Some compacts have focus hold where you can press the button half way down and it will keep those settings. Use a tripod for best results, focus on the flowers, reframe and take the first picture, then take the second immdediately after releasing the button.

Depth of field gives how much is in focus, there is a bit in the camera like the iris of your eye, the smaller the hole in the middle the less light gets in, but the things that are in focus increases so that some nearer and further away things are clear.