Who are you? Can a photograph tell that story? For many years artists have created self-portraits. Vincent Van Gogh painted this self-portrait in 1887. What would it take for a photograph to capture you as a person?
There are several ways for you to create a self-portrait with your camera. One way is to use a tripod or set the camera on a solid surface and use the self-timer shutter feature. Look for a button or menu option on your camera with this icon:

This is the self-timer setting. When you depress the shutter, you camera will wait several seconds before taking the photograph. This gives you time to get into position.
When creating your self-portrait, take into consideration the background.
You may want to place yourself in an environment that says something about who you are. You many also want to use a blank wall or backdrop so that you are alone in the frame. Don't be afraid to do some serious cropping too. That's what Nameet Potnis did in this self-portrait posted to his Flickr stream. His photograph was part of a theme competition for self-portraits on Flickr. Follow that link to see some other interesting photographs.
You should also examine the self-portrait tagged images on Flickr. See how the use of lighting and cropping can create powerful images.