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.