After you pass through Route 102 and battle some Pokémon Trainers, you enter Petalburg City, where your Dad has a gym.
The Poké Mart here has more items than the Oldale Town Poké Mart, including Escape Ropes (they let you instantly exit a cave or other closed area that has wild pokémon in it), X items that boost a stat temporarily during a battle, and Repel, which makes you less likely to encounter Pokémon in the wild.
Before you leave town, you have to go into the Petalburg Gym. Go up and talk to your Dad. Then Wally comes in and asks for a pokémon and says that he will be staying with his family in Verdanturf Town. Your Dad asks you to help Wally catch a pokémon. Wally takes you to Route 102. There will be an automatic pokémon battle, so just watch while Wally's Zigzagoon battles the pokémon. Then Wally will throw a Poké Ball and catch a pokémon. You'll return to your Dad's gym. He will tell you to battle the gym leader, Roxanne, in Rustboro City. Your Dad will battle you after you get four Gym Badges.
Continue your Journey
After you have helped Wally get a pokémon, you can go west from Petalburg City to enter Route 104.