- I discovered your site while I was surfing the net.
- We surf the internet/web.
- I discovered your site while I was surfing on the net.
- We surf on the internet/web.
Are all acceptable?
I would say that adding ‘on’ was used when you wanted to make it clear that you were using ‘surf’ in this particular sense but ‘surfing the net’ is now well established in the language.