It can't be that difficult, right? Your friend/spouse/child asks you to take his/her picture. You have a nice digital camera, so you grab it and take the picture. But you're not happy with the result, and you don't know why. It's in focus and properly exposed; so what's wrong? You've just learned that there's more to a good portrait than getting it technically right.
First, put some thought into the background. It shouldn't distract from the subject. A plain wall, dark green foliage—anything that's simple (without strong lines or patterns) works well. There's nothing worse than a line, pole or branch going through or growing out of the subject's head.
If you photograph someone against a bright background, you may well end up with a silhouette. That's because the brightness can cause the camera to underexpose the subject, making her look dark. You could pop up your Nikon D-SLR's built-in flash or turn on the flash in your COOLPIX or Nikon 1 digital camera to add light to your subject's face, but you'd still have that bright background.
Every Nikon D-SLR and COOLPIX has exposure compensation, so you could overexpose by one or two f/stops or shutter speeds as well. If these methods don't work, then try a different background, preferably something darker than the subject.
Keep in mind that the picture is about your subject. Don't shoot the entire area around them. Get closer by physically moving in or by using a telephoto or telephoto zoom lens. Isolate your subject against that simple background you found. People's heads are vertical, so shoot them that way. Horizontal portraits can look uncomfortable.
Finally, unless you shoot mug shots for the local police department, don't photograph your subject head-on. Have him turn his body a little, maybe 45 degrees away from you, and then rotate his head back to face you. (Tell him, "Don't move your shoulders, just turn your head to me.") It's a nicer, more flattering pose and helps slim people down.