Subject Placement. The biggest mistake many photographers make is to try to shoot a person's whole body, head to toe. Don't attempt this, unless clothes are important (such as a uniform). Instead, focus on the face. The eyes and mouth are the most important features, so start there and work out until you have just enough to represent the individual(s).
Lighting. A standard lighting technique is to position yourself so the sun is behind you and to one side. This arrangement will shine light on the subject's face, while the slight angle will produce shadows to illuminate form. A better approach is to put your subject in a shady area with a shadowed background. Unlike the human eye, photographic film can't easily handle bright areas and dark shadows, as in direct sunlight, so use the shade for a narrow tonal range. Overcast days are usually best for portraits.
Lenses. Use a long lens such as 135mm - the 'people' lens. A wide-angle distorts the face, although it can be effective for parties. Find a simple, mid-toned background and use a wide aperture to throw it out of focus. Center the eyes in the shot, not the head, to provide balance in the shot. When photographing children, crouch down so that you're shooting at their eye-level.
Setting The Scene. Try to set-up your camera ahead of time rather than making people wait. Help relax your subjects by engaging them in conversation. Get them to laugh or smile with a joke from the day. Finally, be sure to put yourself in the shot ;-)
-- that's what the self-timer is for!
