Once the script is embedded in a website, it redirects all the links via www.hidelinks.net - except for the sites that were excluded when generating the script. In vBulletin, for example, you can include the script code in the footer of the global templates (Styles&Templates - Global templates - Footer). In Wordpress, use the footer.php.
Since the script can only anonymize links that have already been loaded at runtime, it's a good idea to place the code as close to the end as possible. Otherwise, links that appear after the script code would not be redirected via www.hidelinks.net.
Using the www.hidelinks.net referrer removal service is quite easy:
For example: http://www.hidelinks.net/?www.google.com produces an anonymous link to www.google.com which prevents the original site from appearing as a referrer in the logfiles of the referred page.