Such good answers already here - I'll just add that my ds has grown in this skill so much!

We had to talk about how to get on the Internet, and use the "Favorites" links. We also talked about skimming subheadings, bolded words, words in blue being clickable, the table of contents on the page, pictures/captions, etc. We also had a good talk about how the Internet is something to monitor just like any other media device.

This helped my dh and I set some important ground rules for computer use. Every family is different, but these were the main rules we decided upon...
1. Dc always need permission from us to use the computer.
2. The amount of time dc may be on the computer is decided by us, and is never to exceed 45 minutes a day.
3. Computers (like TV's/DVD players) must always be used on the main floor in rooms open to everyone (this keeps everyone accountable as people are constantly walking through or in the rooms the computers are in).
4. Chat rooms are off limits.
5. Internet use is with a parent nearby watching and is minimal.
6. We decide which computer games may be used (we've thrown gifts of games we consider inappropriate).
These are the main rules, but I know this will be a work in progress. We have also talked about the Internet being an amazing but dangerous invention. It can connect people worldwide, it can provide so much information at the stroke of a key, but it can also be a temptation - for too much time being wasted on it, for looking at or reading things that are sinful, and for assuming accuracy that may not be there.
My ds has learned to research using the Internet, books, encyclopedias, concordances, and dictionaries via HOD. He knows how to find answers to questions he has, and so many skills along the way. I love how HOD moves dc along in their skills from year to year, while offering options about how to go about using resources. I hope you can find a balance in teaching research skills too!
In Christ,
Julie