Learn French: Il est dangereux de surfer sans le moniteur. - It is dangerous to surf without the instructor.

Because this is an impersonal expression. When you use il est (it is) to make a general statement followed by an adjective and an infinitive, you connect them with de. If you were describing a specific noun you just mentioned, you would use c'est and à. For example: Cette vague est énorme. C'est dangereux à surfer. (This wave is huge. It is dangerous to surf.)

Could I say C'est dangereux de surfer instead of Il est dangereux?

Yes, absolutely. In everyday spoken French, people usually say C'est dangereux de surfer. The form Il est dangereux de... is a bit more formal and is the traditional written standard. Notice that both use de when stating a general rule or fact!

Does surfer mean surfing the web or surfing on water?

It works perfectly for both! You can say surfer sur internet (to surf the web) or use it for the water sport. In this sentence, the presence of a moniteur (instructor) makes it clear we are talking about the water sport.

What is the difference between a moniteur and a professeur?