Typically, a search box is nothing more than a form with a text input. In order to do anything, that form must be submitted to your (a) server, which must then perform the search and return the results. It is not a “simple” process, and it will depend entirely on how your particular site is designed and run.
Especially since you currently have no server-side scripting for your site, you might be interested in using google’s site search service instead.
edit – Paulie_D beat me to it. : )