Instructions
Go to Goldenrod City and enter the Pokemon Gym. Beat the Gym Leader, Whitney, in a battle. This unlocks the Pokeathlon.
Head to Johto's National Park area and then walk west. Follow the path until you enter the Pokeathlon Dome.
Speak to the woman at the counter to select an event in which to compete. Events are broken into the skill, speed and strength categories. After picking an event, select three Pokemon to compete. You are provided with instructions for each event before beginning it.
Perform well at the event to earn points. Coming in first place nets you 100 points. If you do exceptionally well, you earn bonus points. Continue winning events until you have earned 3,000 points.
Walk up to the prize counter in the upper right corner of the Pokeathlon Dome on a Monday, Wednesday, Thursday, Saturday or Sunday. Speak to the attendant and then scroll through the list of available items. Select the Shiny Stone to buy it for 3,000 points.