Some photographers dismiss head and shoulders shots as easy because there is no requirement to control the environment. This is valid to a point, but really good examples are difficult to capture. The main challenges are finding suitable light and novel compositions. Where possible, position the subject in diffused light and use a reflector or a touch of fill-flash to control contrast and put highlights in the eyes. Red-eye is not normally a problem provided the flash head is at least ten centimetres from the lens. Move around the subject to find the most flattering and interesting angles. It is not essential for the person's head to fill the frame, so explore ways of placing the subject off-centre and using space asymmetrically. Compositions of this type tend to be more interesting than standard centred shots.
Half profiles, where the subject turns slightly to one side, have more depth but depth of field may be limited in poor light. Focus on the eyes and control depth of field carefully. Remember that too much out-of-focus shoulder in the foreground may prove distracting.