I'm crossblogging this from a blogpost I made for the ecollaboration blog: David tells us browsing and contribute anonymously to the internet is a basic skill that parents should teach their children. There is a open source software that you can download on TOR. TOR is an anonymiser tool. It makes use of a network of intermediate computers so that nobody knows from where you are connecting and to which websites. You will find the instructions- which are quite easy on the website of Torproject.
You can watch David explain this system:
If you want to know more about anonymous blogging, Global Voices has put up a technical guide for anonymous blogging which you can find here. It explains more steps like choosing pseudonyms.