* The Old Man with Side Duck doesn't teach Surf. He's just a quirky character you encounter in Goldenrod City, and his primary function is to teach you the "Side Duck" maneuver, a way to dodge attacks in battle.
* You get Surf from the Pokémon Fan Club. You can find the Pokémon Fan Club near the Goldenrod City Department Store. After speaking with the president of the fan club, he will teach you the Surf HM.
Here's how to get Surf in HeartGold:
1. Go to Goldenrod City.
2. Find the Pokémon Fan Club. It's near the Department Store.
3. Talk to the President. He's the man in the red shirt and blue hat at the back of the room.
4. He will teach you Surf.
Remember, you'll need a Pokémon who knows Cut to get through the forest path to the Fan Club.