Log in to the PGL and click "Online Competitions" on the main page.
Find a competition that is open for registration.
Details of the competition will appear. Select "Proceed to Sign Up" to continue.
Agree to the conditions and regulations for the competition and select "Sign Up."
If successful, you'll see a message that confirms your registration is complete.
As long as you have a Pokémon Trainer Club account and your Game Sync ID is registered in Pokémon Global Link, just wait until the signup period (10/18 0:00 UTC - 10/25 23:59 UTC) and follow the steps above. After signing up, download your Digital Player ID into your game, and register a battle team for the competition. Go here for more information.