Creating a search function isn't something I'd advise if you don't know what PHP / MySQL is - it's not an overly complicated task but not one that I'd advise on doing straight away.
MySQL is a database that's very popular in web applications. It can be used for other uses as well, but it's most popularly used on the web. The posts in this forum most like get saved in a MySQL database (and if they don't they easily could.) You can use it to store information dynamically, rather than just on static web pages.
PHP is a programming language that ties in very nicely with MySQL and allows you to create dynamic content - again using this forum as an example, when you select to view this thread the PHP code would retrieve all the relevant posts from a MySQL database, and output the HTML to be displayed in your browser. It's one of the most widely used languages for web applications, and definitely worth learning.
One thing though, if you're using a free host they don't always support execution of PHP scripts. If they don't work then that's probably why!
Have a look at http://www.w3schools.com/PHP/DEfaULT.asp
- that's a good place to start, it's a reputable tutorial and when you get to a certain point you can learn about using it with MySQL as well. It's very different from HTML though, so be prepared to look at it from a different approach than you have been. Be careful when searching around the internet for PHP tutorials, there's some really good ones there but a lot of bad ones written by people that don't really know the language that well - they're usually not that difficult to spot, just keep an eye out