You'll find Waterfall in the ice cave... you'll meet a man there who's staring down at an item. Grab the item and it will be Waterfall.
inside the ice cave when travelling to blackthorn city
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you use waterfall at the Pokemon waterfall or the battlefield.
In HeartGold, you can find the HM Waterfall in the Ice Cave.
Basically All you need is surf and waterfall. You cross the waterfall and leave the cave. That is about it.
In the Ice path, there is a guy. there is a pokeball with the HM waterfall below him get it, and he lets you keep it
When you go through ice path, halfway through there will be a man asking you to retrieve his item on the other side of a patch of ice. Get it for him and he will let you keep it: HM waterfall!