go to canalave city and challenge the gym leader
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surf left of jubilife to canalave
Surf is HM #3. :-)
Get the HM Surf then teach it to a pokemon.
Read the inscription at the back of the Celestic Town Ruins, the Village Elder will join you and give you the Surf HM.
You unlock the HM move Surf when you beat Fantina. Before that, you go to celestic town and you will meet Cynthia's grandmother in the ruins she will give you surf.