Instructions
Travel to an area where Wobbuffet will appear, such as the Dark Cave on Route 45 or Cerulean Cave outside of Cerulean City.
Walk around in either of these areas until you have an encounter with a wild Wobbuffet. In either area, Wobbuffet is a rare Pokemon so you will encounter several other Pokemon before a wild Wobbuffet. To speed up the process, run from each battle until you encounter a Wobbuffet.
Attack the wild Wobbuffet using your best Pokemon. Wobbuffet is weak against Bug Type and Dark Type Pokemon, so plan your Pokemon Team and strategy accordingly.
Use a PokeBall once Wobbuffet is sufficiently weakened. If the Wobbuffet does not stay inside the PokeBall, attack it again and then try another PokeBall. Eventually you will be able to force the Wobbuffet to stay inside the ball, adding the Pokemon to your roster.