With the exorbitant amount of information available on the internet, it is difficult to keep a clear view of what is relevant, what is reliable, what is original and what is not. Although students these days are extremely tech savvy and used to using the internet for all kinds of information, they may not necessarily know how to evaluate and filter the information to their purposes. Therefore, this is an area of researching that needs some attention in teaching, since nowadays there is just no way around the internet (especially Wikipedia).
In order to make students more aware of the pitfalls of obtaining information from the internet and in order to highlight the abjection of plagiarism (and making them aware that this is actually sometimes very easily spotted, since teachers use the internet too…), one could as a teacher practice with them in class. For instance, one could use Delicious to collect bookmarks for a certain topic and make the log-in available for the whole class. In this manner all students can contribute tags and bookmarks to a certain topic and these can then be evaluated in class. If the teacher is particularly knowledgeable in the topic, he or she could on purpose add bookmarks containing partly wrong information for the students to spot. An example of a plagiarism (for instance a translation rip-off) could also be added.
In sum, rather than trying to avoid that the students use the internet for their research, guide and support them in making this research more targeted and valid.