Zoom is Your Friend
One of the most fundamental principles of photography is the use of zoom. Zooming does not only make the subject bigger--it also makes the photo more dynamic. If the subject is too small, then people will feel distant from the subject. Below is an example:
Images (c) Jang Photography
These photos are both exactly the same except for the way they are cropped. The bottom one is more dynamic because the flower fills up more of the frame than the first one. Usually, you want to zoom in as close as possible to your subject, unless you purposely wish to show space or a panoramic view. I also like to zoom out a bit when shooting photos with the mood of melancholy/loneliness/depression. However, even in those cases, you cannot make your subject too small, or the photo will lose its impact.
Here is another example (photo of yours truly):
Which photo is more interesting?
(c) Grace Chai. Used with permission
The photo on the right is cropped a lot closer and is much more dynamic than the one on the left. A person viewing the image on the left will not be as drawn into the photo as a person viewing the image on the right. One thing to keep in mind when zooming in on a portrait is to make sure the head is not cut out. If you are going to crop some of the head, then make sure that the head is cropped out on two sides of the frame (like the photo on the right). Also, be careful not to crop a picture at the joints of a person--in other words, don't have the frame cropping out part of the person's arm at the elbow.
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What To Keep in Mind When You're Shooting
You will want to crop a picture using the zoom on your camera rather than computer software because cropping with software will make you lose pixels and thus, information. Therefore, utilize the zoom function on your camera! This is an important principle to remember; when you're taking a photo, ask yourself, "Will this look better if it is cropped? If so, how much should I zoom in?" Experiment with the zoom to see which length is the best--or, if you're not sure, just take the same photo at differen lengths. You can always determine which one is the best when you download your pictures onto your camera. With digital photography, you can take as many photos of a scene as you want and then pick out the ones you like. This is one of the great advantages of digital photography.
Happy shooting!