In order to take a good portrait you absolutely need good lighting. 'Good lighting' isn't necessarily the same for everyone – everyone's face and features are different so you will find yourself wanted to highlight some features more than others.
Avoid using a flash at all costs, to begin with, otherwise you will just end up with a flat snapshot image of your shockingly bright subject's face on a black background.
Side-lighting is flattering on most people. Experiment with having the light closer for a harder image and farther away for a softer look. Larger lights will also give a softer look. If the light is too bright try hanging some white muslin (or another thin white material) between the light and your subject to soften the light.
If you have the light very close to your subject it will create a lot of harsh shadows and your background will be very dark, while having your light farther away will spread the light between your subject and the background.
Experiment with moving the light around the subject to create different shadows. If you place a harsh light overhead you will find that your subjects eyes may be cast in shadow; to counteract this simply have them hold a reflector under their chin to reflect the light upwards and fill the shadows. A reflector can be something as simple as a white sheet of card although coloured card also gives some interesting effects, you can also use mirrors and aluminum foil for variation.