Every weekend you can see great sport photos in the news papers. Although you may not have close access to professional athletes, amateur and children's sports are very good opportunities to take great shots. Often you can come very close to the action. I use a 70-200mm light sensitive (f1/2.8) telephoto lens mounted on a Canon 7D and tripod which I use as a monopod. I shoot at ISO 400, and at least at 1/2000 sec in RAW. This set up gives me very satisfying results. It is essential to take multiple shots per second when the action is unfolding. A lucky one shot is quite unlikely. Having said that, this does not mean you should just fire your shots at any given time, with the idea "the more, the better". If you do this, you will run into the risk of going through your memory cards and batteries quite quickly. Moreover, you will need to go through a lot of photos after the game, which will take a lot of time.
In order to get more shots right, you need to understand the game. For soccer, you can often get nice shots when the goalie kicks out the ball high and multiple players are fighting for the ball in the air and on the ground. Another idea is to shoot the players celebrating a goal. I made a video about a soccer match I shot and you will see how I applied some of the guiding rules for sports photography.