Instructions
Go to Celestic Town.
Find the cave with the Galactic Grunt blocking the entrance. Battle and defeat him; he has a Level 25 Beautifly and a Level 27 Croagunk.
Enter the cave and face the pictures of the Pokémon on the wall. Press "A."
Accept HM03 (Surf) from the old woman who will come into the cave.
Use the Hidden Machine to teach Surf to one of your Pokémon. Only water-type Pokémon can learn Surf.
Head to Lake Verity.
Walk up to the edge of the water and then press "A." You can now surf on the water on your Pokémon's back.
Surf out to the islands with the caves.