The Location
Walk through the towns until you reach Route 35. You will come into the National Park area located on Route 35. Arrange your Pokemon party so that you have fighting or grass-type Pokemon characters available. These are strong against bug-type Pokemon and will ensure good catch rates to obtain a Caterpie.
Enter the Contest
Walk up to the man wearing a red suit to enter the Bug Catching Contest on a Tuesday, Thursday or Saturday. These are the only days available to catch a rare Caterpie Pokemon in the grass. The man in the red suit will equip you with 20 sport balls to use to catch the bug Pokemon. You have 20 minutes to catch the Pokemon bug you desire.
Find Caterpie
Run through the tall grass to find wild bug Pokemon to start a battle. Weaken the wild bug Pokemon character using moves such as hypnosis, sleep powder, stun spore, false swipe or thunder wave if you have them available. These type of moves work well to obtain Caterpie with the sport ball. You can catch one Pokemon at a time. If it's not a Caterpie, replace it as you search through the tall grass. Even if you choose not to keep other bug Pokemon, their information is added to your Pokedex.
The Catch
When you finally encounter Caterpie, weaken him with fighting or grass-powered moves from your Pokemon. When his health bar is low, throw a sport ball at Caterpie to catch him and add him to your Pokedex. Caterpie has a 20 percent rate of showing up in the tall grass. This is the highest of all the bug Pokemon available in the contest.