You can apply to become a Professor by taking the Professor and Organizer exams. Much of the information covered in the exams can be found at:
Play! Pokémon Tournament Rules and Resources page: https://www.pokemon.com/us/play-pokemon/about/tournaments-rules-and-resources/
Team Compendium's Compilation of Official Rulings: http://compendium.pokegym.net/compendium-bw.html
For more detailed information about getting started, visit https://www.pokemon.com/us/play-pokemon/organize/become-a-professor/.
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