Afterwards you can travel along Route 203, battling Trainers and picking up items. Right here is the first area where you encounter wild Abra. It may be useful to know that they have a 5% of holding a TwistedSpoon, an item that can enhance the power of any Psychic-type moves your Pokémon may have. However, it is recommended that you come back later with a Pokémon that knows an item-stealing move, such as Trick, to collect this item in order to make it easier to get.
A hiker greets you at the entrance of Oreburgh Gate. He gives you HM06 (Rock Smash), but you can't use it outside of battle until you have the Coal Badge. Proceed east and you have the option to battle a Camper and Picnicker, respectively. If you chose Chimchar as your starter, catching a Psyduck in this tunnel and raising it to learn Water Gun may be a big help in the upcoming Gym match.
Note that the basement level of Oreburgh Gate is inaccessible until you can use Rock Smash. After getting through the tunnel, you'll arrive in Oreburgh City.
Oreburgh City is the location of your first Gym challenge... but the Gym Leader isn't awaiting your challenge: He's in Oreburgh Mine, located south of the Pokémon Center. From this city, you also have the option of heading through the north exit to Route 207 to find some new wild Pokémon.
In one of the houses here, there is a woman, Hilary, who will trade you her Abra, nicknamed Kazza, in exchange for a Machop, which you can catch on Route 207. Additionally, remember the Oreburgh Mining Museum, as it will be useful if you find Fossils later in the game.
After walking down the steps leading to the inside of Oreburgh Mine, you will enter a rectangular room. Upon reaching the large block of coal in the center of the room, turn right, and then walk south until you reach the end of the wall, at which point you should see a red-haired man in a mining helmet a few steps to your left. Talk to him, and he will introduce himself as Roark, the town's Gym Leader, and show you how to use Rock Smash. He then tells you that he will be back at the Gym, ready to challenge you. Exit the mine and head to the Gym.
Interior of Oreburgh Gym.
This Gym, as you have probably figured out, specializes in Rock-type Pokémon. The toughest Pokémon you'll face is Level 14, so be prepared. Rock-type moves are supereffective against Bug-, Flying-, Ice-, and Fire-types, so obviously you don't want to use Pokémon of those types in this battle. Also, you will want Pokémon with Water-, Grass-, Fighting-, and/or Ground-type attacks. You should bring a few Potions to this battle, just in case.
After retrieving Roark from the mine, you may enter the Gym and battle the two Trainers, or you can take the first set of stairs, go across the bridge and walk up the second set of stairs to avoid battling. Then, you may challenge Gym Leader Roark.
Roark's first two Pokémon shouldn't be too much trouble. The Geodude knows Rock Throw and Stealth Rock, and its best stat is Defense. Stealth Rock will damage any Pokémon you switch into battle (Most Pokémon will lose 1/8 of their HP if hit. It will damage more if the Pokémon is weak to Rock-type moves, and less if it is resistant.). Rock Throw is just an attack, which is thankfully somewhat inaccurate. A good Grass- or Water-type attack will likely take Geodude out in one hit. Roark's Onix may be a bit more challenging, mostly because it has more Defense and Speed, and can use Screech to lower your Pokémon's Defense in addition to Rock Throw and Stealth Rock. If you get hit with Screech, you may want to switch before Roark sends out Cranidos. Cranidos is rather fast for this point of the game, and has a scary amount of Attack that will do massive damage with Headbutt or Pursuit, particularly if Onix used Screech or if Cranidos previously used Leer against you. Try switching in a Pokémon with Intimidate like Shinx to lower Cranidos's threat, but beware of Stealth Rock. It doesn't have the best defenses though, so one Water, Grass, or Fighting-type attack should send it out for the count.