After you get four gym badges, you can return to Petalburg City and challenge the Normal type gym where your father Norman is the leader.
This is a Normal-type gym. Normal-type pokémon are weak to Fighting moves. In addition, if you have Ghost-type pokémon, they are immune to Normal-type moves. However, Normal-type pokémon are immune to Ghost moves, so your Ghost-type pokémon will need to have some non-Ghost attacks.
Some of the trainers in this Gym use Delcattys that know Sing. It can be very annoying to have to wake your pokémon up over and over again, so if you have any pokémon with the Vital Spirit or Insomnia ability, it might help. You can also get Chesto Berries and give them to your pokémon to hold.
Not only that, but these Delcattys are female and they know Attract, AND they have the Cute Charm ability, which will cause male pokémon to fall in love with them and not be able to attack. Use female pokémon against them, or a pokémon with the Oblivious ability, since they are immune to infatuation.
The Petalburn Gym has several rooms. In each room, there is one trainer who specializes in using a certain battle item at the start of the battle, boosting a stat of the pokémon. In the first room, you can either go into the Speed Room on the left or the Accuracy Room on the right.
The trainer in the Speed Room uses an X Speed on a level 27 Delcatty (level 26 Swellow in Emerald). The worst part about this room is dealing with Delcatty's Sing move. With its increased speed, it is likely to go first, UNLESS you use a move like Quick Attack in order to go first. Even worse, Delcatty knows Attract and has the Cute Charm ability, so be sure to either use female pokémon or pokémon that have the Oblivious ability, since they are immune to infatuation.
Afterward, if you go through the door on the left, you enter the Zero Reduction Room (Confusion Room in Emerald), and if you go through the door on the right, you enter the Defense Room.
The trainer in the Accuracy Room uses an X Accuracy on a level 27 Delcatty (level 26 in Emerald). This room is probably a bit easier than the Speed room. The Delcatty's moves won't miss, but if you have fast pokémon, they can probably move before Delcatty does. This makes it less likely that Delcatty will use Sing before your pokémon can attack. But, as stated above, be sure to protect yourself against infatuation if possible.
Afterward, if you go through the door on the left, you enter the Defense Room, and if you go through the door on the right, you enter the Recovery Room.
Zero Reduction Room/Confusion Room
In Ruby and Sapphire, the trainer in the Zero Reduction room uses a Guard Spec on a level 27 Linoone. Guard Spec prevents stat reduction, so for example, Sand Attack would normally reduce the opponent's accuracy, but in this battle, the Guard Spec prevents Linoone's accuracy from decreasing.
In Emerald, the trainer in the Confusion room has a level 26 Spinda that inflicts Confusion on your pokémon. Switch out your pokémon or use Restores or berries to cure the confusion.
Afterward, you can go into the Attack room.
The trainer in the Defense Room uses an X Defense on a level 27 Linoone (level 26 Wigglytuff in Emerald).
Afterward, you can go left to reach the Attack room or go right to reach the One-Hit KO Room.
The trainer in the Recovery Room uses potions on a level 27 Linoone (level 26 Slakoth in Emerald). You will need to deal a lot of damage in a short amount of time in order to defeat this pokémon. Try using sacrifice moves like Overheat or Selfdestruct.
Afterward, you can go into the One-Hit KO Room.
The trainer in the Attack room uses an X Attack on a level 27 Zangoose (level 26 Vigoroth in Emerald). Try using a type of pokémon that is strong against Normal attacks, such as Ghost, Rock, or Steel.
Afterward, you can go to the Gym Leader's room.
One-Hit KO Room
The trainer in the One-Hit KO Room uses a Dire Hit on a level 27 Zangoose (level 26 Zangoose in Emerald). Dire Hit increases the chance that the opponent will do a critical hit. Try using a type of pokémon that is strong against Normal attacks, such as Ghost, Rock, or Steel. It can also be helpful to use a pokémon with the Sturdy ability, so even if it gets hit with a critical hit, it will survive.
Afterward, you can go to the Gym Leader's room.
Gym Leader Norman
For the battle against Norman, I STRONGLY recommend that you bring a pokémon that knows Protect or a similar move. Two of Norman's pokémon are Slakings, and they each have the Truant ability, which means that on every other turn, they do nothing. You can defeat them easily if you attack on the turn when they do nothing, then use Protect on the turn when they attack. Protect will always work, because you are not using it consecutively. If you do this properly, they won't be able to do any damage to you at all.
Also, Norman's level 31 Slaking knows Focus Punch, a Fighting move where the Slaking focuses its energy before attacking. But if your pokémon can attack first, you will break the Slaking's concentration and it won't be able to attack. Therefore, if you use a move like Quick Attack, you will always break Slaking's concentration and prevent the attack.
All three of Norman's pokémon know Facade, a move that becomes much stronger if the pokémon that uses Facade is poisoned, paralyzed, or burned. So don't inflict those status conditions on Norman's pokémon!
After the Battle
After you defeat your dad, he gives you the Balance Badge, increasing the defense of all of your pokémon, and allows you to use Surf outside of battle. He also gives you TM42 Facade, which, as mentioned before, is much stronger if the pokémon using Facade is poisoned, paralyzed, or burned.
After the battle, go outside and go into the house to the left of the gym. Talk to Wally's father to get HM03 Surf. You will need to have a pokémon that knows Surf if you want to reach the next part of the game.
Back in Littleroot Town, you can talk to your mom and she will give you an Amulet Coin since you defeated your dad.
I recommend going to Mauville City and talking to Gym Leader Wattson, who is walking around outside. He gives you the Basement Key and asks you to shut down the generator in New Mauville. Now that you can teach Surf to a pokémon and use it outside of battle, you can reach New Mauville. Surf under the bicycle path in Route 110 to reach the northeast cave beyond the water. Use the basement key on the locked door to enter New Mauville. You can complete the generator quest if you want, but more importantly, I recommend catching Voltorb and Magnemite in here. If you are really lucky, you might encounter Electrode or Magneton. These are very helpful in the next gym.
Otherwise, feel free to Surf in the areas of water that you couldn't explore before. There are many good items and new areas to find.
When you are ready, go east from Mauville City and Surf across the water to reach Route 118.