After going through the south part of Route 104, you reach the forested area of Petalburg Woods.
Explore the Route
In the Petalburg Woods, you can catch Wurmple, Zigzagoon, Taillow, Slakoth, Shroomish, Cascoon, and Silcoon.
If you go to the southeast part of the forest, a boy there tells you that you can find hidden items on the ground sometimes. Go into the grass to the right and check on the empty spot in the center to find a hidden Potion.
Go south from there to reach an area of Route 104 that you couldn't reach. You can get a Poké Ball there.
Go north to enter the woods again, then go west. As you follow the path, you will encounter Bug Catcher Lyle. He has three Wurmples.
Northwest of Lyle, there is a Paralyze Heal in the grass.
Go east from the Paralyze Heal and you will find a scientist looking around for a pokémon. Then a Grunt from Team Magma (in Omega Ruby) or Aqua (in Alpha Sapphire) runs up to steal some papers from the scientist. It's up to you to battle the grunt and protect the Devon Researcher!
The Grunt has Poochyena. After you defeat him, he admits that they're trying to steal something in Rustboro City.
The Devon Researcher gives you the Exp. Share. It's automatically turned on, so all pokémon in your party will get experience after battles or after you capture a pokémon. If you want to turn this off, open up your bag and go to the Key Items pocket, then select the Exp. Share, then choose Off. You can turn it back on the same way.
After that, the researcher heals up your pokémon and goes back to Rustboro City.
Go northwest from where you battled the researcher and you will run into Bug Catcher James. He has a Nincada.
North of James, you find an Ether.
East of there, you find a tree blocking the path to the east. You will need to have a pokémon that knows Cut in order to cut down the tree, so be sure to come back later.
Go north from there to leave the woods. As you leave, a member of Team Aqua/Magma will call somebody to report that you interfered with their plans. After the cut scene, you reach the northern part of Route 104.