You don't need surf to get through the distortion world. You only need the move strength.
Get the HM Surf then teach it to a pokemon.
You get Surf from the elder of Celestic Town.
rock clim surf streng
Surf is HM #3. :-)
On water.
you surf
Yes, it can.
A gymleader i think...
beat the fifth gem leader than you get the Hm surf
find the waterfall and surf into it ( you dont need HM Waterfall)
you get it from cynthia's grandma in celestic town
By using the HM Surf