To get the HM Surf you need to speak to Darren in the middle of Kanto Safari in Fuchsia City. You need a ticket to get to the safari and it cost 20,000. From when you enter the safari go straight down and you will see a little island with a small walk way with the npc Darren standing there. Surf lets you move across water tiles. You do NOT need to teach it to a pokémon in order to use it, however you DO need the soul badge.
Pokemon Planet - Free Pokemon MMORPG
Kanto Walkthrough, Pokemon Planet Wikia
Tom Kenny - IMDb
Poké Ball - SmashWiki, the Super Smash Bros. wiki
Surf, Pokemon Planet Wikia
How to Find the Move Waterfall in Pokémon Black: 7 Steps
How to Find the Move Waterfall in Pokémon Black: 7 Steps
Surfing Pikachu - Rising Rivals - Pokemon
Koopa Troopa - Super Mario Wiki, the Mario encyclopedia
Pokemon Planet - How To Get Surf!
