Instructions
Travel to the National Park, located north of Goldenrod City, on a Tuesday.
Approach the counter and speak with the man behind the counter to enter the Bug Catching Contest. Press "A" to select the Pokemon you would like to bring into battle with you.
Head north into the large patch of tall grass.
Walk around the tall grass until you encounter a wild Butterfree. There is only a 5 percent chance of encountering a Butterfree and a 1-in-8,192 chance of encountering a pink, "shiny" Butterfree. If you encounter other wild Pokemon, either defeat them to gain experience or run away from battle.
Battle Butterfree and weaken it with strong attacks until its hit points are in the critical red zone. Use status-changing moves such as "Hypnosis" and "Thunder Wave" to make it easier to catch.
Throw a Poke Ball at Butterfree to capture it. If it breaks free, continue throwing Poke Balls until it is captured.