After the second badge, (If you haven't already), go to the cave at the north side of town. Teach flash to one of your Pokemon and use it. You will find Steven at the end of the cave, and you will give him the letter. He will also give you steel wing, which is a pretty good move that most flying types can learn. After that, go back to Mr. Briney. He will now give you the option to go to Slateport. Do it. Once there, you will have to battle a lot of trainers on the beach. Then, you will be in Slateport. Go inside the shipyard (The big gray building) go straight ahead, and when you see a man at his desk, talk to him. Then go back outside and to the oceanic musuem. Then pay the fee and go upstairs. You will have to beat two team aqua members. After that, give the goods to the man and head out of town, upwards. You will have to battle a couple people. Once you see the purple house, you have to look for an old lady walking like straight under the bike path. Once you find her, go past her and you will be on the Low Road. You will have to battle your rival, either Brendan or May, then some other people. Once you get off, you will be in Mauville City. Beat Wally out front of the gym, then go inside, figure out the puzzle, (It's really easy.) and challenge the gym leader. Hint: Save your game right in front of the gym leader. That way if you lose, you can just turn it off. The gym leader is pretty hard. When you beat him, he will give you the knuckle badge. Hope I helped! :)
at the gym
Go to the Pokemon league.
it's in the woods between the first gym badge and 5th gym badge
by beating the fourth gym leader
The fourth one.
Dewford Town.
you can find it near the second gym badge and its in a cave.
on dewford island. go by boat
at the gym
every second gym leader will allow you to use higher level Pokemon
Go to the Pokemon league.
Destroys picachew
the ground gym
Pokemon league
Beat the gym leader
you travel to lavavine town
Fortree city.