After defeating the Gym Leaders of Mossdeep Gym, you should go south from Mossdeep City to reach Route 127.
Catch Pokémon
While Surfing, you might encounter Tentacool, Wingull, and Pelipper. If you fish with the Old Rod, you might find Tentacool and Magikarp. With the Good Rod, you might find Tentacool, Magikarp, and Wailmer. With the Super Rod, you can catch Sharpedo and Wailmer.
Explore the Route
In the northwest part of the route, there is shallow water where you can find a Zinc. In Emerald, you can also find a Rare Candy in this area.
South of that, in Ruby and Sapphire, Bird Keeper Byron is standing in another patch of shallow water. He has Swellow and Pelipper. In Emerald, there is Bird Keeper Aidan, who has Swellow and Skarmory. There is also Cooltrainer Athena, who has Manectric and Linoone. She might join Aidan in a Double Battle.
In the northeast of the route, there is an island with some Secret Base locations. There are also three fishermen there. Jonah has Tentacool, Wailmer, and Sharpedo. Roger has Magikarp and Gyarados. Henry has Tentacool (in Ruby and Sapphire only), Tentacruel, and Carvanha.
South of that area, in Ruby and Sapphire only, you can find Triathlete Connor in the water. Connor has Wingull and Staryu.
In the southeast of the route, there is another island area with more Secret Base locations. There is also Black Belt Koji, who has Machoke.
If you dive in the dark spot in this area, you can go to the northern spot underwater and surface in a new area where there are trees. You can find a Carbos there.
Underwater, you can find a hidden Star Piece, Heart Scale, HP Up, and Red Shard.
When you are ready to move on, go south to reach Route 128.