Instructions
Ensure that you have one empty space in your Pokémon party as well as a Pokémon with high happiness (any Pokémon you've had for a long time, such as your starter Pokémon, should have high happiness.)
Use a Pokémon equipped with "Surf" to travel north from Five Island.
Veer to the northwest when you come to a maze of rocks marked as the "Water Labyrinth."
Continue left, navigating through the simple maze until you reach a small island occupied by an old man.
Walk onto the beach and talk to the old man to receive a mysterious egg.
Take roughly 3000 steps with the egg in your party and it will hatch into Togepi.