Simple php search engine for a site

[creeaza]

I have a Ro based language site: http://www.creeaza.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.creeaza.com/didactica/didactica-pedagogie/index13.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,