The building west of the entrance is quarters for those working at Devon Corporation. On the second floor, talk to the little boy to get a Premier Ball.
To the west of the Pokémon Center is a house. Talk to the man there to get HM 01 (Cut).
Head east past the Center to the Pokémon Trainer's school. Talk to the teacher here to get the Quick Claw.
NOTE: Depending how you interact with Tommy and Marc, you can fight both of them at once in a Double Battle. To do this, you come directly in the line of sight of both of them at once. You can do that, if you want, by coming straight up on the left side of the maze.
Once you beat Roxanne, you'll get your first badge, and TM39 (Rock Tomb).
After the gym
Now that you have your first badge, step outside, to see the same Magma or Aqua grunt that you fought in the forest running away from Devon Corp. and the worker you saw earlier running after him. You can head over to the Pokémon Center and Heal if you want. Then head up to the north where you'll meet the worker, who'll give you a job to do - pursue the Aqua/Magma Grunt, who stole some Devon goods, and retrieve it from him! To get to the grunt though, you'll have to traverse through Route 116.
Emerald Players have the privilege of fighting their rival near the Pokémart after they run their errand for the Devon Corp. man. This battle isn't mandatory, since he/she will ask you if you want to fight him/her.
