Cynthia's Grandmother. She will tell you what badge is needed also. Kinda funny. I looked up the SAME question before... Hope that helps!;)
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Surf is HM #3. :-)
Get the HM Surf then teach it to a pokemon.
beat the fifth gem leader than you get the Hm surf
HM03
The elder in Celestic Town. It's part of the plot (You need surf to get farther in the game, significantly), so it shouldn't be too hard.