Various things from addressing the problem directly if possible (block the IP address range they use to scrape your content with, insert JavaScript to strip the content client-side depending on the domain it's being served from), to changing their search engine behavior (canonical meta tags, contact the search engine to let them know, build up links on the web to make your site higher ranked).

The more sophisticated and popular the copycat site is (scraping from a distributed network, stripping most HTML tags, etc.), the harder it becomes, and the only thing is to contact the search and hope they can manually mark your domain as the authoritative one. Your success may vary according to your popularity/importance.