Sports mode and auto focus are a good place to start with. The biggest step up in shooting quality will come from a good lens. And you can sink some coin into a good one. Best thing I can tell you is to shoot a lot and experiment with different locations and practice with manual mode. Once you get a better understanding on ISO and F-Stop and shutter speed you can really dial in what you are shooting. Also if you camera allows you to shoot in RAW format give that a try, but you will need photo editing software that can convert the image into a jpeg.

Hope that helps a little.