HTML is Hyper Text Markup Language, so all it really does is formatting. To search through your website, or actually all the files in your website, you'll need to use perl (cgi) or PHP to do the actual searching. You'll also want to have this stored in some database (MySQL or PostgreSQL) to reduce the amount of work that your server has to do. Your search will work better if it only has to search through the database, rather than searching through all the files for every search.
I don't know how you define convenience, but this is really the most efficient way to do it, and practically speaking, the only way. It may not be brain-dead simple, but it's not that difficult to set up a PHP-MySQL powered search function. Check out
PhpDig. If you can set up Apache, you should be able to get PHP to work with MySQL without too much trouble.
Enjoy!
--- Cerbere
[edit] And BTW Welcome to LQ.org! [/edit]
[edit2] An even better (simpler) search engine is
here. [/edit2]