Free php search engine for my site

Hello all,
I have a Italian based language site: http://www.epertutti.com with articles on different categories.

I want to implement a simple php search engine for my website on pages like this on the top right corner:
http://www.epertutti.com/italiano/index59.php

Note: I keep all texts (title, body articles) on a mysql database.

Is there a possibility to integrate Google Site Search?
How can i do that?

I need some code suggestions, to make this script run fast.

Thanks all,