Lighting. Lighting. Lighting. The more unusual, the more it will captivate the viewer. Avoid DIRECT sunlight.
FOREIGN BODIES: Elements in the frame that do not belong (e.g. background of your aunt’s picture has half a chair!).
Do not use a flash indoors! Instead, stabilize yourself. Prop your elbows on a table, sofa or something that does not move. Don’t try and use another person, no matter how stable you think they are.
If you camera permits it, increase the “film speed” of the camera. In digital cameras this means changing the sensitivity of the sensor. Keep in mind however, that this leads to an increase in noise. You can safely increase it to 400 ASA without noticing much of a difference.
Get close to people!
For portraits, look through the viewfinder around the subject (person), see anything but the person and maybe another 6″ of space? Yes? Take a giant step forward. Repeat. The idea being that you want to draw attention to the subject and not the chair, carpet, picture frames… You get the idea. Keep it simple. Make it a routine to look around in the viewfinder just before you click. Once you “get it” it will become second nature. I promise!
Use a flash outdoors!!
Make people stand in the shade or blocking the sun so that YOU are facing the sun then use fill-flash. If you have one of those, “auto-flash” point-and-shoot cameras, then find the little round photosensor window on your camera (that detects the amount of light), and block it carefully with your fingertip. Usually, that should make the flash fire when you release the shutter. Be careful though, with this technique unless the light is not very strong (overcast weather), you may land up with an overexposed image. Of course, if that happens, back off the finger a bit and try again. What do you have to lose? A few minutes? Remember, the best thing you can do with digicams is to shoot like heck and ask questions later!