What you have got to do is clear the psyduck blocking the path outside Solaceon Town and then make your way through the path towards Celestic Town then battle the galactic grunt blocking the cave enterence. Once you have go in and look at the markings at the back and a lady who you have to give the old charm to will give you surf. To use it outside of battle you must defeat the gym leader Fantina.
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surf left of jubilife to canalave
go to canalave city and challenge the gym leader
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.