Route 203 is a short route with a few trainers. Battle them to level up your Pokémon. At the end of Route 203, you'll enter Oreburgh Gate. This cave is straightforward; just follow the path. You'll encounter a Hiker who will give you TM95 (Rock Smash), but you won't be able to use it outside of battle until you get the first Gym Badge. Continue through the cave to reach Oreburgh City.
Upon arriving in Oreburgh City, your rival, Barry, will challenge you to a battle. His team will vary slightly depending on your starter. After defeating him, he'll suggest you visit the Gym. However, the Gym Leader, Roark, is not there. You'll find him in the Oreburgh Mine, located in the southeast part of the city. Head into the mine, speak to Roark, and he'll return to the Gym. Now you're ready for your first Gym Battle!