There are several ways in which you can become familiar with your camera; read the manual and study it carefully, put it in automatic or program mode and shoot without ever learning about its other features, talk to other people who have a similar camera, or pay somebody to teach you to use it. My way to learn about a new camera is to go out and shoot things I have shot before but change the camera’s settings so I can get an idea of what it is capable of doing. In other words, I play with the camera.
Paying someone gets you further ahead than shooting in auto, but you must follow the lessons with lots of shooting on your own to really learn the camera. Reading a manual can teach you lots about the camera, if you can manage to stay awake while reading it. Talking to others with similar cameras, may or may not help you, as most of the people I have encountered do not use the advanced features of their camera. So that leaves playing as the most practical way to learn how to use it.
It is by shooting with your new camera that you become comfortable using it. When you revisit familiar settings, you place yourself in a situation where relaxation makes you more receptive to play than a formal setting. I used to consider the first 10 rolls of film (with digital technology, the first 8 gigs of images) as my way of learning what the camera is able to do. Every shot afterward would be better than the first ones as I could then concentrate on composition and lighting.
Get out and shoot!