One of the biggest surprises of becoming a teacher was not how technologically focused my students were, but how truly bad they are at using technology. Very few of my students grasp usage of the internet beyond Googling, uploading and emailing one another. Even worse, many students have the misconception that the internet is in their wheelhouse, and all answers are but a half-second of typing away.
However, the risk of ruin either via plagiarism, inappropriate content, or simply using incorrect content is great. Therefore, I would teach three basic things about digital citizenship to my kids:
1) Google is not your last stop for research. The algorithms that Google uses to generate results can be manipulated and do not take accuracy into account for their returns. Researching using only the first page of a Google search is inviting terrible trouble.
2) Assume that nothing you find is free or in the public domain. Plagiarism and cheating have become a rampant problem with our students because of the ease of locating answers, passages or whole essays about their selected topics of inquiry. Too many students have fallen into the trap of simply copy-and-pasting information and passing it off as their own, without any thought regarding citations or source references.
3) Use your best judgment. Many unscrupulous people and places exist on the internet. Do not fall victim to any of these sorts of people. Much like you don't venture into bad parts of town or down a dark alley, do not do so on the internet.
Finally, as far as parents go, I would stress the need to not let down their guard when their children (even high-school age ones) are using the internet. Make use of programs like NetNanny or other such applications to monitor their children's activities on the internet. There is simply too much predation and actual crime that comes forth from the virtual world to assume that your child is safe or on-task, left to his or her own devices.
Hope this helps. Good luck in the classroom!