Surf on the Internet & Surf the Internet ,which is grammatically correct?
I wrote the essay for IELTS ,one of the sentences goes like this:
"This is because some private information such as personal data and account passwords might be revealed when we surfing on the Internet or browsing different websites."

Some teachers in my country told me that it should be " Surf the Internet",but other teachers said that it should be "Surf on the Internet"
Can any English speakers helps me with this question ,please?also,if there's any wrong or weird expression in this sentence,please don't hesitate to correct me ~thank you!
I want to express it in a natural way without grammar errors ,thank you!

Question

Surf on the Internet & Surf  the Internet ,which is grammatically correct?
I wrote the essay for IELTS ,one of the sentences goes like this:
"This is because some private information such as personal data and account passwords might be revealed when we surfing on the Internet or browsing different websites."

Some teachers in my country told me that it should be " Surf  the Internet",but other teachers said that it should be  "Surf  on the Internet"
Can any English speakers helps me with this question ,please?also,if there's any wrong or weird expression in this sentence,please don't hesitate to correct me ~thank you!
I want to express it in a natural way without grammar errors ,thank you!

Answer

Both can be correct depending on context. "Surfing the internet" sounds more natural to me. I would never say, "I am surfing on the internet," because even though it is correct, native speakers don't really talk like this, even in formal settings. I would say, "I'm surfing the internet."

"...when we surfing on the internet" is incorrect.
Correct: "...when we *are* surfing on the internet."
Another correct option: "...when we're surfing on the internet."

In order to use an "-ing" form of the verb "surf," you have to use the helping verb (modal auxiliary) "to be".
Correct: We surf. 
Correct: We are surfing.
Incorrect: We surfing.

Answer

Where I live, 'surf or surfing the Internet'  is most common.
Don't get too technical about it, surf the 'net works too.
As Brian stated, omit 'on'