Instructions
Finish the Johto region by acquiring all eight gym badges and defeating the Elite 4. This will give you access to the Kanto region of the game, where Seafoam Island is located. During the course of your adventures in Johto, you will acquire the "Surf" ability in Ecruteak City. This allows you to travel across water.
Travel to the Kanto region by going to Olivine City and boarding the ferry. You will arrive in Kanto at Vermillion City.
Play through the Kanto region until you have access to Pallet Town. Find it by traveling along Route 01.
Travel along Route 21 from Pallet Town using the "Surf" ability. Route 21 leads to the Island of Cinnibar.
Go to the Pokemon Center on Cinnibar Island to restore your team before using the "Surf" ability again east of town. This takes you along Route 20, where you will encounter lots of swimmers that challenges you to battle.
Keep following Route 20 until you reach an Island with a cave entrance. This is Seafoam Island. Climb the ladder in front of your character as you enter the Seafoam Island Caves to enter the gym. Head further into the caves if you want to explore and catch new Pokemon.