Keep moving east on this route and defeat all of the trainers. Grab the repel that is lying on the ground in the southern pathway. Be careful, as you can initiate double battles by having two trainers see you at the same time. If you want to avoid this, just make sure that you aren't spotted by two at once. When you reach the house, head up and left towards the maze. Click on the small trees, and if you have a Pokémon with cut, they will use the ability to clear the trees. Make your way through the maze, defeating all of the the trainers and grabbing Ether and the berries.
Once you are done that, attempt to head into the cave at the eastern end of the route. An old man will tell you that his Pokémon Peeko was taken by Team Aqua. Head into the cave and go up, grabbing the Pokeball. Then head left and fight the Team Aqua Grunt. Defeat him (which is easy), and he will give you the Devon Package and then run off. Exit the cave, and the old man will thank you for returning Peeko to him. Next, take the package back to Rustboro. You will be stopped by the man whom you met in Petalburg Woods, and he will give you another Great Ball. He will then take you to the Devon Corporation offices to meet Mr. Stone, the president. He will thank you for your hard work, and ask you to deliver the package to Slateport and a letter to Steven in Dewford. What a lazy guy. However, he will give you a neat little device known as the PokeNav. This may be used to view a map , among other things.
Once you are done speaking to him, head down all of the floors of the building and out the front door. You will be stopped by a Devon scientist, who will install a new app onto your PokeNav. This will allow you to record the numbers of certain trainers and rematch them at a latter date. You will be asked to call Mr. Stone to test this, so simply go into your PokeNav and select the "Match Call" function. Once you have completed this, it is time to go to Dewford. Attempt to leave Rustboro to the south and you will be stopped by your rival. He/she will register you on their PokeNav, an then ask if you would like to battle. It is optional, however this guide will be covering it.
This battle is a bit more difficult. As a general rule, try and use Pokémon and moves that are effective against the Pokémon you are fighting. If you don't have Pokémon that are effective against the enemy, or are weak to the enemy, then just try and beat them down with your strongest attack, and don't get hit. If you need to, use potions and other items to keep your Pokémon from dying. It is possible to play through most all of the game without using a Pokémon other than your starter, though it is generally easier and more rewarding to level a well rounded and powerful team of Pokémon that compliment each other.