You can obtain 'surf' (HM03) at the Ecruteak City Dance Theater.
The old man from the Ecruteak Dance Theater will give it to you as a reward for defeating the Kimono Girls.
Surf is a big wave that crashes down the foe. It's also a move that lets Pokémon swim accross water.
In Generation II (Gold & Silver/Crystal), the player can freely choose their order of facing Kimono Girls. In Generation IV (Diamond & Pearl/Platinum/HeartGold & SoulSilver), the player battles them in a fixed order, having to defeat all five consecutively.
Check out this Pokémon Shiny Gold Walkthrough including video guides that can work well for both Pokémon Shiny Gold and Pokémon Shiny Gold X Version at Pokemonshinygold.com.
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