Instructions
Speak to Dawn outside the Veilstone Gym. She asks you to help her get Team Galactic out of town and recover her Pokedex. Then she asks you to meet her in the Galactic Warehouse.
Go to the northwest of the city, and enter the Galactic Warehouse. Dawn is waiting, which initiates a dual battle against two Team Galactic Grunts. She gets her Pokedex back, and the rest of the grunts run into the warehouse to hide.
Head west to the satellite dish. There is a man standing in front of it. Speak to him, which scares him off -- dropping the key that allows you to enter Team Galactic HQ and defeat their top trainers.