The most common mistake made by photographers is that they are not physically close enough to their subjects. In some cases this means that the center of interest—the subject—is just a speck, too small to have any impact. Even when it is big enough to be decipherable, it usually carries little meaning. Viewers can sense when a subject is small because it was supposed to be and when it's small because the photographer was too shy to get close.
Don't be shy. If you approach people in the right way, they'll usually be happy to have their picture made. It's up to you to break the ice and get them to cooperate. Joke around with them. Tell them why you want to make the picture. Practice with people you know so that you are comfortable; people can sense when you aren't.
                               -From Nationalgeograghic Photograghy Tips 

There are several ways to approach self-portraits. One way is to frame an interesting composition and then, with your compact camera mounted on a tripod or another means of support, use the self-timer (if your camera has one) to trip the shutter after you get into position in front of the lens. Just remember that a self-timer will give you a very limited amount of time to get in position (usually 10 seconds). It helps if you can get a friend to be a stand-in until you can be there, or mark your spot with tape or chalk.
             -From shutterbug
You can also capture a self-portrait by supporting your camera, then frame your picture and focus with a stand-in. Place a mirror just behind the camera, and do your final posing in the mirror. This method also requires a self-timer, or a remote triggering device if your camera has one. Once again, if you use a self-timer, you'll need to get into position before it goes off.
                                          -From shutterbug