This looks like a standard pop-up menu. If you just need sub-menus for each link, you should be able to just add them in like this:
<ul id="menu">
<li><a href="#">Home</a></li>
<li>
<a href="#">Categories</a>
<ul>
<li><a href="#">CSS</a></li>
<li><a href="#">Graphic design</a></li>
<li><a href="#">Development tools</a></li>
<li><a href="#">Web design</a></li>
</ul>
</li>
<li>
<a href="#">Work</a>
<ul>
<li><a href="#">Work 1</a></li>
<li><a href="#">Work 2</a></li>
</ul>
</li>
<li>
<a href="#">About</a>
<ul>
<li><a href="#">About 1</a></li>
<li><a href="#">About 2</a></li>
</ul>
</li>
<li>
<a href="#">Contact</a>
<ul>
<li><a href="#">Contact 1</a></li>
<li><a href="#">Contact 2</a></li>
</ul>
</li>
</ul>
No other CSS changes should be needed. No special id's should be needed. Let us know if it works.