I think this is a great question, and I look forward to others' answers. My own response is too general, maybe, but I believe it is very important to pay attention to what the internet is actually good for, and what it isn't good for. I believe the same applies to computer technology and digital technology in general. It is very easy to get caught up in the slickness and the smoothness of the internet and so on, but this is often just an illusion, and other ways of doing things are more reliable and efficient in the long run.
For instance, I just wrote about the new Kindle e-book technology on my blog, and argued that while many digital technologies are very beneficial, the book made of paper is really rather remarkable for its versatility and ease of use, compared with digital books and note-taking.
So my answer is that a primary cognitive skill when using the internet is to keep very healthy ties to any good cognitive habits you have developed in 3-D, and to be able to pick it up and drop it according to its actually usefulness in relation to other possibilities. It is hazardous to not have a pen and paper with you when using the internet!
I apologize if this answer missed the mark.
All the best,
Mike+