There are many factors that can go into a blurry sports picture.
If the photographer was using a telephoto lens, then the shutter speed need to be 1/ the focal length as a guide to avoid blurriness from camera shake.
Example if you are using a 200 mm telephoto, try to shoot no slower than 1/200 of a second shutter speed.
As Dan suggested, increasing the ISO of the camera allows for an increased shutter speed at the same apeture openning.
If you are trying to follow quick action, the camera focus may not be able to keep up with the action especially if it is moving towards or directly away. Some cameras feature a "continuous focus" feature to help with objects that are moving quickly away or towards the camera. Also, decreasing your apeture will increase your depth of field and give you a better chance of keeping objects in focus.... but this will slow down your shutter speed which may give you problems with the telephoto lens.
If you are close enough, using a flash may help but typically the shutter speeds will be 1/60 of a second. This may not work with a telephoto because of the "shake" issue and the object's distance may be out of range of the flash.
The quick answer, keep the shutter speed as fast as possible and possibly prefocus the camera where you think the action will be so you don't have to rely on a slow autofocus feature.
