It starts with detecting the theft via services like Google Alerts and Mahalo's Plagiarism Detection tool, or even just following the trackbacks that automatically come from some content scraping sites.
Other steps include bringing in third parties, be it the advertisers (if the site is making money off of duplicate content), the domain hosting service and the search engines themselves.
Bailey notes that you should exhaust all options for getting the plagiarist to remove the content on their own before turning to these "authorities," and to be aware of how each prefers to receive the dispute info (via fax, email, etc.) and what documentation is needed for them to take action. He also provides links to DCMA policy info and document templates.