Here's tips on how to catch a wild Caterpie in the wild.
1. Caterpie's capabilities.
Caterpie is a fairly easy Pokemon to capture in the games. Bring along flying types and fire types to cover yourself against it and always try to make sure to have False swipe to help bring their HP, hit points to one very easily.
2. Use Status effects like Sleep Powder and so on.
One of the best ways to capture Pokemon is by using status effect moves on them. Capture a Pokemon like Butterfree or Venasaur and use moves like Sleep Powder on them to be able to easily put them to sleep. You can also use other Pokemon to help put them to sleep as such as well. Things like Hypnosis can be used by Pokemon named Gastly, Hypno, Gengar, and so on as well. Stun Spore is also an excellent move to use and utilize on a Pokemon to help capture it easier in the wild while playing Pokemon. A better move that has the same effect as Stun Spore which causes paralysis is a move named Thunder Wave. Lot's of Pokemon can learn this move like Alakazam, Ampharos, Pikachu, Jolteon, and so on. If you are able to stun and paralyze your opponent then the act of capturing them becomes child's play in that moment. The chances for catch rate and capturing the Pokemon increase significantly. The last possible decent methods for capture is possibly poison and maybe frozen here and there. Poison is generally not always recommended since this heightens the chance of the Pokemon being able to lose and faint before you can even capture it. The frozen status condition is very rare and difficult/hard to pull off so I would not rely on this condition to inflict a good and useful status condition on the Pokemon you wish to capture.
Bring lots of Pokeballs unique and quantity wise.
Be sure to always buy lots of Pokeballs to further progress capturing the Pokemon you wish to catch. Quick balls are always useful to throw on the first turn of a battle since that's the higher success rate of usage for them. Next you can always spam Pokeballs for cheap to test the waters and see how hard it is to catch this particular Pokemon. Ultra balls and Great balls are always the best option for high success rate of any Pokemon in any general area. If at nighttime or in a cave Dusk balls are the way to go. And other good options are such like Net balls for Water and bug types and Heavy balls for heavy weighted Pokemon as well too.
Those are the best tips to capture Caterpie and other general Pokemon. Feel free to manage and capture Pokemon the best you can and always have fun with Nintendo and playing Pokemon no matter what.