Background, this rule is an easy one. To make your subject more of a subject, you want it to stand out in the shot. To insure this always try to keep your background as uncluttered as possible.
Check out the two images below, both are of the same subject. Left is the view that I had of the flower when I first noticed it. After photographing it I noticed that it gets lost in the background so I then took a minute to find just the right angle to where the background was as clean as possible.
Tip. If you like photographing flowers try keeping a black piece of foam board in your kit. Hold it just far enough behind your flower so that it is out of focus (Depth of field) your colors will jump off the screen!!