Here's how to get it:
1. Complete the Veilstone Gym.
2. Visit the Pokémon Fan Club on the west side of town.
3. Speak with the member near the back. He will ask you to go on a treasure hunt, which requires you to follow the clues on the walls.
4. Follow the clues. They are written on the walls in the Fan Club, and they lead you to specific spots in Veilstone City.
5. After finding the last clue, return to the Fan Club member who will give you HM02 Fly.
Remember, you need a Pokémon that can learn Fly (like Starly or Pidgey) to use it in battle and outside. You can teach Fly to your Pokémon by visiting any Pokémon Center and selecting the "Teach HM" option.