Instructions
Go to Goldenrod City, found north of Route 34 in the Johto region. Walk north on Route 35 to enter the National Park.
Talk to one of the clerks at the entrance on a Tuesday, Thursday or Saturday to sign up for the Bug Catching Contest. Unlike the Safari Zone game that usually happens here, there is no cost to sign up for this contest.
Pick one Pokemon from your current team to take with you into the park. Select a Pokemon that knows sleep-inducing moves, if possible. Paralyzing or freezing moves are also advantageous.
Walk around the National Park and look for bugs to catch. When one approaches, try to catch it with one of the Park Balls you got from the clerk.
Use all of the Park Balls to end the contest, or just leave the National Park. Select a bug from those you caught. This bug will be judged. First-place bugs earn you a Sun Stone.