Well to use a search box you need to have it search somewhere, for example a Database. Inside the database you will have stored some data like posts... names... contents or what ever... and with the search box you will search inside this database.
Questions ? you have some sort of database like stored information ? Or is it plan HTMl pages (i see it is :/) so basically it is impossible.
For your site i suggest using a Wordpress like blog... so you can insert data in it... you'll have to add the template of course which will need HTML editing... (you have a control panel to add posts and such) and it comes with a search box that searches inside your database.
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If the design you are using is from zymic you should have copyright on the bottom.. which appears that it has been removed ? I dunno