People are easily the number one subject for photographs. From party snaps, to photos of children and travel shots of family members in front of famous monuments, millions upon millions of people photographs are taken every single say of the year.
Portrait photography is a little different to general people photography. The intent of portrait photography is capture and display something of the 'essence' of a person; to say something about their character, personality, or life.
The three most important things to get right in portrait photography are camera settings, lighting, and your relationship with your model.
Camera settings for portrait photography
Because taking portrait photographs is all about a person's face (or if it's a wider shot, their head-and-shoulders), classic portrait photography settings seek to remove anything distracting from the background of the shot. This mimics the effect of looking at someone's face from very close up, and makes the subject 'pop' (this is photographer-speak for 'stand out and capture attention').
The way to achieve a distraction-free portrait photo is to use a wide aperture, often as wide as possible (f/2.8 or f/4 are popular choices). Wide apertures produce a shallow depth-of-field, which renders anything far from the plane of best focus - i.e. the background - as a soft blur.
Aside from a wide aperture, the only other important setting is ISO. This should be as low a number as possible (e.g. ISO 100), as higher ISOs will lead to digital noise, which is particularly ugly in a portrait.
There's one offshoot of portrait photography where the recommended settings are different, and that's environmental portrait photography.
Environmental portrait photography seeks to show a person in their 'natural habitat', which is often their workplace. Here you want to show the background, so a smaller aperture is appropriate.
Lighting for portrait photography
Lighting in portrait photography can be as complicated as you like. Professional portrait photography is almost always done in a studio, where the lighting can be 100% controlled. If you're reading this, chances are you don't have your own photography studio, so let's discuss a simple lighting scheme you can set up at home.
First, position your model at a window. The light coming from the window should be bright, but not direct (i.e. not coming directly from the sun). You model should be facing you, side on to the window. Light from the window light will obviously light up the side of their face that is closest to it. Then, position something on the other side of your model that will bounce reflected light from the window onto the other side of their face. Anything white or reflective will do, for example a piece of white cardboard or a sheet of aluminum.
Now you have a basic, flattering light scheme, with the main light source on one side of your model's face, and 'fill' light from the reflector on the other. Don't forget that you should frame the shot close enough that the reflector is not in the shot.
Interacting with your subject
Portrait photography inevitably says something about the relationship between photographer and subject. Unless you're shooting professional models, the hardest thing about taking portrait photos is not in fact camera settings or lighting, but ensuring that your model is comfortable and relaxed enough to give you good results. A model who feels awkward, uncomfortable or self-conscious will not photograph well.
Often the best strategy to relax your model is simply to engage them in conversation, as this will take their mind off the camera. They'll probably get more comfortable with the process after you've rattled off a few shots, so schedule a decent amount of time and plan on taking your best shots towards the end of the session.