Generally speaking, portrait photography affords the photographer the greatest challenge in his work. Unless you’re working with a professional model or an unusually cooperative and expressive personality, then you will find photographing people a task to be tackled with care.
In the studio the photographer has the challenge of bringing out the personality of the subject. Try chit-chat to get the subject at ease. If this fails, remember to keep a light mood.
The photographer needs to remember to keep a positive and lighthearted demeanor when working with average people. Do not give the impression that your job is a serious issue of expressive art, no matter how much you may feel that is the case. It will just put a shell over the subject. Also, do not be introverted. A shy subject is hard enough to deal with; a shy photographer makes his own job much more difficult than it should be.
On-site photography lends some more freedom to a photographer, especially if the subject is involved in some activity in which he or she is comfortable. Shooting a portrait on site is apt to bring out more genuine expressions and moods than those conjured in the studio. It’s easier for a subject to "forget" the photographer is present when he is in a comfortable environment.
Something to try when shooting portraits is to experiment with lighting. See what kind of effects you get when using side-light rather than direct light. Whenever possible, avoid a direct flash (like the ones built in to camera bodies) when taking portaits. Try using the natural lighting of a scene to your advantage.
If your subject is not a specific individual, but you are just out photographing people in general, try to stay inconspicuous. People interacting naturally with other people or their environment are much more expressive than people posing for a picture. No matter who your subject is, they will likely not act naturally when they know a camera is aimed at them.