After you find Steven in Granite Cave and give him the Letter, you can ask Mr. Briney to take you to Slateport City.
When Mr. Briney stops the ship, you start in Route 109. You can explore this area if you wish. There is a house here where you can battle trainers to win 6 Soda Pops.
There are several trainers on the beach: Sailor Huey, who has a level 14 Machop (or a level 12 Wingull and level 12 Machop in Emerald); Tuber Ricky, who has a level 14 Zigzagoon (level 13 in Emerald); Sailor Edmond, who has two level 12 Wingulls and a level 12 Machop (a level 13 Wingull in Emerald); and Tuber Lola, who has two level 13 Azurills (one is level 12 in Emerald).
Additional Emerald Trainers
In addition, in Emerald, there is Tuber Hailey, who has one level 13 Marill. Tuber Ricky might do a Double Battle with Hailey or Edmond depending on where you are standing when they see you. Ricky has a level 13 Zigzagoon. In Emerald there is also Tuber Chandler, who has two level 12 Tentacools. He might join Lola for a Double Battle.
Go north to enter Slateport City.
You can do a lot here. There is a market, a place to participate in Contests, and a person known as the Name Rater, who will change the name of a pokémon that you caught yourself. The Name Rater won't change the name of a pokémon that another player caught and then traded to you.
There is an item you can get later if you buy a Harbor Mail in the Poké Mart in Slateport. Be sure to do that.
Go into the contests building and talk to the girl to get a PokéBlock case. Go into the back room of the contests building and talk to the guy in the southwest corner to get TM41 Torment. In the Pokémon Fan Club building, you can get a Soothe Bell if you have a pokémon that has high friendship toward you. Friendship increases when you level up your pokémon and walk around with it a lot.
Deliver the Goods
Go east and find the building with ships next to it. Go inside and walk north. Talk to the guy at the table. Then go outside and go north, then east to the building across the small bridge. Go inside and pay to enter. Talk to the Team Aqua/Magma Grunt who is turning around. He gives you TM46 Thief. Then go upstairs and talk to the guy in this room. You will try to hand over the goods, but two Team Aqua/Magma grunts attack. The first one has a level 15 Numel in Ruby or a level 15 Carvanha in Sapphire and Emerald. The second grunt has a level 14 Zubat and a level 14 Numel/Carvanha.
Now that you fought the Team Aqua/Magma Grunts, you can use the north exit of town to go to Route 110.