Photographing people can be a very intimidating and daunting task! After all, there is implicitly a lot of pressure on the photographer when taking people photos as your subject is often awaiting to see the results and final images! Being a great people photographer often starts with being a good people person. If so, then you are well on your way!
People photos fall into two categories: portraits and candid. Either can be made with or without your subject's awareness and cooperation.
However near or far your subject, however intimate or distant the gaze your camera casts, you always need to keep in mind the elements of composition and the technique that will best help you communicate what you are trying to say.
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.