So, this is a pretty broad thing to talk bout with photography. There are so many different kinds of action shots that you can take, and just as many tips about how to place your camera, where to focus, and all of that other good stuff. The main thing to remember is that action shots can pass you like a bullet, so you have to be prepared at all times to press the button and take that photo. You will miss a lot of moments if you blank out, so really try to focus in when you expect a shot to come out of nowhere. There are a few things you can do to help with this sort of stuff.
One thing you can do is to pre-focus where you believe the object will appear. Pick a good spot that will make for a great picture, and then sit there and wait for that object to get to the spot you picked. A quick burst of fast shutter speed shots should do the trick, depending on how you want to capture that object. You can do a little bit more research about pre-focusing to find out what exactly you should aim the lens at and the different ways the camera will focus based on the light levels of the area and other factors.
Another tip to remember is to give the object room to move, or keep a good distance so you can let the object move into your view instead of having to move your camera to get it in focus. This will prevent any blur in the photo if you want to freeze the image, and will reduce the amount of blur on the object in focus if you still want to have a sense of motion in it. Always keep in mind that depending on how the object will me moving, you will want to have the camera at an angle. Of course, you can always edit the image afterwards, so that is not so much of a big deal if you have some decent editing software that you know how to use effectively.
This may sound a little bit weird and counterintuitive, but try to keep both of your eyes open as well. I can tell you that from my experience with taking photographs of soccer matches, closing one eye really messes up the way you see distance, especially If you are trying to follow the ball to get a picture of someone about to shoot the ball. If you are taking pictures of people, always try to get the face in the shot. This makes the photo more dramatic and really gives a feeling of emotion. You also want to try crouching down, as lower angle shots tend to make things look bigger in the shot and really draw out the distance. You may have seen photographers crouch down when taking photos, and even though it may look a little funny to see them move while bent down, the photos they capture by doing this are worth the looks.