As you explore Striaton City, you will discover Fennel's house, where someone is blocking the stairs to Fennel's room. Not only that, but there is someone blocking the entrance to the Striaton Gym. He says that the gym leader went to the Pokémon School.
You need to go to the Pokémon School and talk to Cheren, who is standing at the blackboard. He will say that the gym leader must have just left. He'll challenge you to a battle.
Cheren has a Purrloin and the starter that is strong to your type. This shouldn't be too difficult, but don't put your starter into battle, because Cheren's starter has learned its first elemental move, which will be super-effective on your starter. Try to have your other pokémon fight Cheren's starter.
Once you defeat Cheren, a gym leader will be standing outside of the Striaton Gym. He will say that you can challenge the gym now, but he says that at this gym, your pokémon will have to fight against a pokémon that has super-effective moves against your starter, so he suggests going to the Dreamyard to train your non-starter pokémon.
Go to the Dreamyard, which you can reach by going northeast. You will encounter some trainers here, and you will also meet someone who will ask if you want his pokémon. Accept this generous offer to receive one of the three elemental monkeys. You will receive the type that is strong against the gym leader's pokémon (as well as being strong against Cheren's starter.) The monkeys are Pansear (Fire), Panpour (Water), and Pansage (Grass).
Train up your pokémon if you wish, and then head to the Striaton Gym.