Instructions
Visit the National Park building on Tuesday, Thursday or Saturday, if you have not yet acquired the National Pokedex. If you have obtained the National Pokedex, visit the park on Tuesday. The National Park is located to the west of Route 36 and north of Route 35. Once you enter the building, talk to the man to the left of the door. He will give you 20 Sport Balls to catch Pokemon with.
Run through the grass in the park. You will eventually see Caterpie. Once it appears, damage it with an equal level Pokemon and capture it using a sport ball. Do not catch anymore Pokemon in the park.
Enter the building on the right side of the park. Talk to the man inside the building. If you have time left in the contest, he will inform you. Select Yes to end the contest. The contest winners will be announced. Although you likely will not place, you can still keep the Pokemon.