Here is some information on the rule of thirds, which is a way to frame pictures that you are going to take:

Link: Rule of Thirds

Good video that explains it:

Changing the shutter speed is unfortunately, not something most point and shoot cameras allow us to do. Generally we need one of the expensive Digital SLR cameras for this task. So why is shutter speed important? Well depending on the situation it may or may not be. A fast shutter speed is used for pictures with movement and/or action, such as a soccer game. A slow shutter speed is great for portraits. If you took a picture of someone running with a slow shutter speed, the picture may appear blurry and/or their could be a train behind the person running because the movement wasnt captured correctly. For instance, when you see a picture on the cover of sports illustrated of someone hitting a tennis ball, it looks as if everything in the picture is stopped because they used a fast shutter speed. Thus if you intend to use your digital camera for any type of action shots, it may be worth your money to invest in an SLR instead of the regular point and shoot cameras that most of us have.