After you drop off the Devon Goods in Slateport and go north through Route 110, you reach Mauville City, home to the next Gym.

Explore

Go east from the entrance and walk behind the fence to reach the hidden X Speed.

Go into the house north of there and talk to the guy at the table to get HM06 Rock Smash. After you get the Gym Badge from Mauville Gym, you will be able to use Rock Smash outside of battle. This will allow you break some types of rocks that are blocking your path. In addition, sometimes Rock Smash causes a wild pokémon to appear.

Go west and enter the house next to the Poké Mart. If you have a Harbor Mail, you can give it to the girl in this house to get a Coin Case. You can use it to win coins at the Mauville Casino. You can use the coins to buy dolls and TMs.

Go into the house east of the Pokémon Center. This house is the bike shop. Talk to Rydel to get a bike. You can choose the Mach Bike to ride up slopes and cross cracked floors safely. You can choose the Acro Bike to jump over certain things. It doesn't matter what you choose, because you can come back to Mauville and change your bike at any time.

After getting your bike, feel free to go south to Route 110 and go up to the bike path. Just enter the big house at the north or south end of the route. There are more trainers on the bike path.

Go to the Pokémon Gym. Wally is here. He is the one you helped catch a pokémon earlier in the game. He challenges you to a battle. He has a level 16 Ralts. After you defeat him, you can enter the Mauville Gym.