Start by going to the Olympic Games and enter Olympic Mode. Select the Foot Race event on High difficulty. Follow along through the tutorials until you get to the actual event.
To run down the track, alternate pressing the "A" and "B" buttons as fast as you can. The more speed you can get, the better. At random intervals you will get a prompt to press "X" or "Y". Doing so will make you hit your opponent and slow him down. If you fail the prompt, you may be hit and slowed down yourself.
Close to the end of the race you will receive a series of random button prompts. You don't really need to worry about these unless the race is neck-and-neck, in which case quickly enter the button prompts to dive across the finish line.