Help with adding Javascript to PHP code

Hi,

I have created a drop down menu through Fireworks and would like to apply it to my header menu. The header menus are made up of my categories so I only want this drop down menu to apply to one category that has children categories.

My files are called mm_css_menu.js and header_menu.css

The PHP code that is for the header menu is as follows:

<div id="header-menu">
<ul>
<?php if (is_home()) { ?>
<li class="current_page_item"><a href="<?php echo get_option('home'); ?>/">Home</a></li>
<?php } else { ?>
<li><a href="<?php echo get_option('home'); ?>/">Home</a></li>
<?php } ?>
<?php wp_list_categories('sort_column=name&amp;title_li=&amp;depth=3'); ?>
</ul>
</div>

I just need to be pointed out what I need to add to display children categories and where to add the javascript code.

Am I correct in thinking this is the Javascript code I need to add in:

<script type="text/javascript" src="mm_css_menu.js"></script>
<link rel="stylesheet" href="header_menu.css" type="text/css" />

The menu item is Products that needs the drop down menu if you need to see my site it’s http://abcbabyland.com/blog/

Thanks for all your help.

Wendy