I have always been fascinated with plants and flowers particularly as subject for photography and taught myself just about everything I know. Consequently, I have devoted a good portion of my life to photographing them. As much as I would love to pursue it full time, photography is a hobby, not my career.
Unlike almost all professionals, and many amateurs, I take my pictures with a simple point and shoot camera, and not a particularly good one at that. My current camera is a Samsung BL103: 10.2 MP, 3x optical zoom, and less than $100. I want everyone to know that it doesn't take a $2000 camera to create beautiful shots. And now onto the flowers.
Although it is very possible to create beautiful pictures indoors, I strongly recommend that you at least begin outdoors. This way, lighting is provided and the whole atmosphere looks more natural, which creates a better picture. Any flower can create a beautiful picture, but a good starting point is a daisy type flower:
A flower with a relatively "flat" center and radiating petals is easy to focus and compose in the photograph. In the picture above, the center of the flower is on the lower third line, and near the left third line. Though thirds certainly aren't a requirement, and a flower more or less centered can create a stunning picture, they are a good starting point. Notice that the angle of my camera to the plane of the flower is probably somewhere between 30 and 45 degrees. I am not coming from directly above, nor flat or underneath. Depending on the aperture, this can create an interesting effect where some of the flower is in focus and some isn't. This can be seen better in this photo:
The angle to the flower is one of the easiest and most effective aspects of the picture to play around with. Another daisy type flower that I shot straight at creates a very different look:

(Note: there is some post processing on this picture to created a filtered black and white effect for the background, but the picture was taken with a 5 MP camera)
Earlier I mentioned some effects of the aperture. This is a very important part of creating a photo that really pops. It makes a huge difference when the background is blurred and out of focus so the eye really focuses on your subject. All 3 of the flowers above demonstrate this. On many cameras, there are extensive manual controls, but my options are pretty limited. I focus as close to the camera as possible, which usually helps. If my focus extends too far into the background, I blur the background on GIMP using layer masks. If anyone is interested I can explain this on another tutorial.
I never use the zoom. I turn on macro mode, and off the flash, and then move the camera as close as I would like to, or can, get to the flower. Generally, I can get within 3 or 4 inches of my focal point before I start to lose it. By not using zoom, I am able to focus better and preserve details of the picture. Then, I can crop and zoom on the computer to create the shot. For example:
As I can only include 4 images per post, I am adding a part to for the second half of the tutorial. Take a look at that as well please!
A partial portfolio of my work is located at
Bashful Bird: Photography and other artistic endeavors
UPDATE:
Part 2 is located here