icetek on "..... How do I make a custom search input and MySQL query."

I want to add a field for Search in Category within searchform.php. A select option box. The select is id=w. So the URL flag would be http://example.com/?s=somekeywords&w=myOption. How do I do this? I'm aware I have to work with MySQL too. Given that a search of the Wordpress source code literally turns up $_POST and $_GET 100 times I am confused as to what is the proper method of doing this.

Thank you.