Petalburg City is the first big city you'll encounter. Heal up at the Pokémon Center and stock up at the Poké Mart, then troop to the gym in the town. It's that building with the brown roof. Head inside and you will meet the Gym Leader, whoi s also your father. He'll say a few words before a boy named Wally enters.
Wally is a lonely boy who would like a Pokemon of his own to accompany him on his way home, for the sake of pure companionship. Your dad, Norman, is more than happy to help. He will lend Wally a Lv.7 Zigzagoon and your services. Follow Wally back onto Route 102, where he will encounter a Ralts. Watch him battle and capture the Ralts. Overjoyed, he will take you back to the Gym and return the Zigzagoon to Norman. He will then leave, and you are free to do the same after a few more words from Dad. You two will battle someday, but not at this time.
There's nothing more to do at the present moment, so head off towards Route 104. As you approach it, a guy in black glasses will stop you and talk for a moment. He will criticize you saying you're a rookie trainer and that you are not worthy and stuff, and will go off. Now that was a bit too much...