For shooting action photography -

For shooting action photography (sports, horse/car race, aviation)

Equipment: Well, as far as I am concerned, it is very likely that you will need a telephoto lens for this kind of photography. There isn't a specific lens that you should use, but the following are choices worth considering:

For Nikon:
the less expensive but sharp AF-S Nikon 70-300mm f/4.5-5.6G IF-ED VR
or the expensive but legendary AF-S Nikon 70-200mm f/2.8G ED N VR II

For Canon:
the less expensive and not really that good EF Canon 70-300mm f/4-5.6 IS USM
or the expensive but sharp EF Canon 70-200 f/2.8L IS USM II

Skills: On your camera, turn the mode dial to shutter priority (S or Tv). This will allow you to adjust the shutter speed manually, but all the others in auto. Use a higher shutter speed in order to freeze the action. Now, it is really difficult to say which shutter speed to use for action photography as there are many kinds of them, but here is a list of 'preferred' shutter speed for the kinds of photography I mentioned in the title:

Sports: at least 1/500
Horse/car race: at least 1/1000
Aviation: at least 1/640

For a more detailed tutorial, please visit here!