Freezing the action and panning are the two techniques used in action photography. Freezing the action is easier. Panning needs a little bit of practice and patience.
Fast shutter speed is used to freeze the action. How fast shutter speed you need depends on how fast the subject is moving, the angle you are looking the subject to past you and how far away you are looking at the subject. For a runner 1/400 is generally enough to freeze the action, but in motorsport 1/1000 is more likely the case. Telephoto lens works well for this technique.
Slow shutter speed is used in panning. Like in freezing the action technique, there are several variables that affects to choosing the right shutter speed. 1/30 is pretty good place to start. Shutter priority mode can be very helpful with this technique. However, you should be careful when using that mode, because your camera meter might not be accurate. If the test shots feels too light or dark, you should find exposure compensation from your camera and use it to compensate your camera meter. In this technique you are following the subject with your camera. If you are located close to the subject, then wide angle lens works perfectly with this technique.