I crop all the time! Rarely do I find a picture that does not improve with a crop. Often, I do several different ones. It really helps to have a high resolution picture for this operation.
A lot of my bike pics are cropped for my 24" wide screen on my computer. Because of this, I end up taking a picture further back due to the typical bicycle height to length ratio.

Like many said, play. With the advent of digital photography, you can do a lot a playing in very short time. My suggestion, if you are a novice, is to use the point and shoot on auto exposure and play with lighting and composition first. Once you feel comfortable, learn about depth of field and play with it.

Zoom or lens focal length variations are worth playing with too. It takes awhile to see the subtleties of the difference between a 85-100mm lens vs. a good 50mm Macro at 1:1 ratio. The perspective changes dramatically. Many good portrait pictures are taken with 85mm lens vs. the 50mm due to the change in the perspective of a person’s face. A fish eye lens, like an 18mm, will really distort the image by spreading it out like a circus mirror.

There are a lot of good basic photography books/articles out there. Read, learn and play.