What? 서핑 가르쳐 주세요? It's not a ve.ry good traslation
They dropped the object particle. 서핑을 가르쳐주세요.
Technically they also made the sentence less complicated, since "how to" is not translated. However, it isn't required. 서핑하는 방법을 가르쳐주세요. = Teach me the method of surfing.
It does make sense. Koreans like to make their sentences as short as possible. You don't have to say "how to" because it's assumed in the context.
I'm Korean. 어떻게 서핑하는지 가르쳐주세요. or 어떻게 서핑하는지 알려주세요 Choose one.