The most frequently used preposition to use with the word internet is 'on'. Sometimes the preposition 'over' is also used. Think of the internet as a bridge or highway for the transfer of information. So you would be 'on' a bridge or 'on' a highway. The preposition 'with' also works but is used in completely different situations. You would use 'with' if you are talking about the internet as something that you have. (With the internet, people can send emails) Also, check out this similar question.
Example: I found an article on the internet. More examples of how to use internet in a sentence can be found here.
