When you press this page's Search button, it triggers a Python script on the server, which in turn builds a "term site:site" site-specific search query and passes it to a selected search provider using an HTTP redirect. You can view and fetch the code of both sides of this interaction here:
this page ⇒ Python script
The net effect displays results in the provider's page. The script uses basic CGI, and its redirect is a simple technique that leverages work already performed by search providers that have crawled the site (invited or not). Assorted tips:
Because this page delegates searches to third-parties, it comes with some inherent caveats. First and foremost, some search providers may both track searchers, and insert ads and unrelated photos in results. In testing, Google's search results for "fortran" at this site included paid ads for compilers, and Bing displayed pictures of pastry chefs for "decorators" (yes, really). Google also disables the Back button in some contexts, for reasons not yet isolated.
In light of such constraints, the privacy-respecting sites DuckDuckGo and StartPage are strongly recommended for users of this page. Of these, DuckDuckGo seems best in terms of search results so far (sometimes finding more than Google), and StartPage seems a close runner-up. Although other search providers can be selected above for comparison, their monetization focus makes them innately perilous, and a "use at your own risk" proposition.
Search would ideally avoid third parties altogether, of course, but a more custom solution is currently outside this site's proprietor's schedule. For more on web search privacy options, see this; or try a web search...