I always thought having "rules" about things like "photo composition" or "songwriting" was strange. There's shouldn't be rules that govern artistic creativity, and I would feel slightly egomaniacal dictating such rules to you now. I do, however, have some tips that have always worked well for me in the past, especially in regards to portraits.
#1 Using Natural Light
I decided to group Natural Light into this Composition blog because I feel that the position of light has a huge impact on how one should compose their photos.
Ok, a few basic tips to get started.
First, if at all possible, try to shoot at either sunrise or sunset. Personally, I don't think I'll ever be awake for sunrise, so sunset has always been my favorite time to shoot.
Keep in mind that sunset goes by incredibly quickly! Make sure that you've given yourself plenty of time to set up whatever equipment you might have and that you're totally ready to roll by the time the sun starts to set.
Here's an example of the light just before, during, and just after sunset. Keep in mind, only twenty five minutes went by between the first exposure and the last.
Notice there's nothing special about the light in the first photo, but by the time we've reached the fourth photo the sun has just hit the horizon line, giving us some really fantastic light. After that, there's a brief period where the light is very flat, and actually quite nice in it's own way. Photographers like Rosie Hardy or Brooke Shaden wait until this twilight to do their amazing work.
Also, take note of the position of the sun. The sun is behind the subject. I can't stress enough how big of a difference this makes. When the light is behind the subject, you can achieve really great highlights, forming a kind of glowing outline around your subject. Now, chances are if the light is behind your subject, there's not going to be any light on the face. This is where using a reflector comes in. If you don't own one of these, just go buy one. http://www.bhphotovideo.com/c/product/639216-REG/Creative_Light_100842_38_White_Silver_Reflector.html It's probably the least expensive and most singularly useful accessory you'll ever buy. Using either an assistant, or a small stand, you can position this reflector in front of your subject to bounce light back into the face.
If you're shooting indoors and stuck for a background, try positioning your subject directly in front of a window. If it's bright enough outside, and you expose your camera for your subject inside the house, you can often achieve a great pure-white background.
2# Where to position your subject.
One of the earliest "rules" of photography that I ever heard was "Don't center your subject". It took my a long time to realize why I didn't always like that rule.
Basically, if centering your subject causes interesting symmetry in your photo, then by all means, center! Also, if you're cropping your photo to a square, that square crop is basically begging you to center your subject.
So, there's nothing wrong with centering!
I could get into the rule of thirds, leading lines, etc. But I'll let you in on something… The photographers who take the best photos (and I am by no means including myself in that group), take TONS of photos.
Here's your scenario. You've got a great model, and a fantastic background. You take a photo. It sucks.
This happens all the time. It's your job to experiment until the photos stops sucking, and starts being awesome!
If it helps, develop a sort of "check list" of things you can try.
Shoot from a lying position.
Shoot from above your subject.
Position your subject on the left.
Position your subject on the right.
Just try stuff!
One last piece of advice, then I'll stop being all preachy for today. Always ask yourself, "What am I taking a photo of?" If you can't answer that question, the photo is probably not worth taking.
In the photo below, what am I taking a picture ok? If the answer was just "Times Square" I don't think the photo would have been as successful. However, I'm taking a picture of a couple having their photo taken in Times Square, which I feel focuses the photo a little bit more, and forces Times Square to be the setting, as opposed to the subject.