More often than not, people simply point their cameras at other people and click off! Few of these will ever look at the photos in the 'review' and decide to shoot the same frame again; still fewer (and innocent) might appreciate good portraits but can't really say what goes into capturing those perfect moments.
I have yet to master the art myself but I feel I can definitely give a few pointers for beginners.
The photo on the right is probably one of my personal favourites. It was shot in a small village during a casual photo trip that a few of us had gone on. The powerful emotions in the kid's eyes were not so easy to catch - I had to strike up a small talk with him and then click 4-5 frames to get the one I wanted.
Firstly, shooting multiple frames is almost always a good idea. Secondly, notice that almost the entire frame is filled with his face, avoiding any distracting background. Initially while taking portraits we tend to try and 'get everything' or 'fit the face / half body' and in the process loose the essence of portraits - to capture emotions. For example in this photo, part of the kid's face (ear and small portion of head) is not in the frame; but by avoiding that, the focus of the viewer goes straight to the kid's eyes - or at least that was the intention!
This is one of the techniques used in portraits - the effect of good composition. Most of the times, any good camera put on one 'auto' or 'portrait' modes will take care of the rest of the stuff.
Another technique used to eliminate the background distraction is taking advantage of what is called the 'depth of field'. Simply put, this factor decides how much or rather which portion of the frame will be in sharp focus and which will be totally out of focus, creating the desired 'blur' in the background. The details of aperture, focal length etc are left aside for this beginner's guide. The first step is getting the composition right! Once that is done, the above mentioned factors can be easily played with to get better results.
Portraits are meant to bring out details, to bring out the finer aspects of the picture, to get the viewer 'involved'.
Almost everyone around has a digital camera these days with more features than many care to use! This aspect of photography, however, hardly requires any special features and yet is accepted to be one of the most challenging ones in photography!