I've never taken a good photo. I tend to look like this:
1) The coy bob
Stand arm's length away from a mirror. Tilt your head, chin back / forehead forward, until you can see some of the white of the eye below the iris.
This creates an optical illusion which foreshortens the face, making the lower half appear smaller. Because women have smaller jaws then men, this feminizes the face (not always the best idea for men with small chins). It also makes the eyes appear larger, as they are closer to the camera than the mouth.
This should be done subtly. Part your lips slightly and open your eyes a bit wider, with your eyebrows slightly raised; the image people use is of a baby sparrow in expectation of being fed. If you have a particularly wide mouth or thin lips, slightly purse the lips, pulling the corners in as if about to say "oh."
This is difficult to master and, done incorrectly, can look odd. Opening the lips causes the lips to look fuller and opening the eyes makes them look larger (as does the eyebrow raise).
3) The smizing squinch
Tyra Banks coined the term "smize" - smiling with the eyes, but it's been around forever; you can see it in the Mona Lisa, for example. While the idea is correct, many people do it incorrectly - often sparrowing! The proper way of doing it is to raise only the lower eyelid or "squinching;" smile and you'll see that you tend to do this automatically. As step one created a space between your iris and lower eyelid, this step eliminates it.
Because one can focus only on the eyes or on the lips, smiling with the eyes and not the mouth causes a tension in the portrait that is interesting.
4) The head clock tilt
Now, instead of your head being straight up-and-down, tilt the head from "12 and 6 o'clock" to 1 and 7 or to 11 and 5. If you look at painted portraits, the eyes are almost never level and this mimics that.
Faces are never completely symmetric. This tilting of the head disguises that and causes the viewer to think the face is more symmetric than it actually is.
5) The wrist watch
Lastly, put the camera on the mirror you're facing, covering your eyes. The mirror allows you to get the camera steady and parallel. Now, look at the wrist of the hand holding the camera and take the photo.
Studies have shown that people prefer to see smiling faces looking directly at them, but prefer to see faces not in a toothy grin looking to the side. It gives an air of mystery to the photo.
Ultra Loony update
2 days ago