SharePoint handles the rendering of navigation for you, assuming that you want SharePoint to manage your navigation bar. There are quite a few caveats to allowing SharePoint to manage your navigation if you intent to brand it, mainly in how you set up your site structure. When it comes to branding, the primary problem you are going to encounter is that by default most of your primary static links (Staff, It and Organization) in your example will actually be on the second level in your nav list.
<ul>
<li><a href=”#”>Home</a>
<ul>
<li><a href=”#”>Staff</a></li>
<li><a href=”#”>IT</a></li>
<li><a href=”#”> Organization </a></li>
</ul>
</li>
</ul>
SharePoint also adds a bunch of divs and classes that may cause something like SuckerFish issues. Most nav plugins I have worked with will attempt to hide any non-toplevel list items, so your nav bar would only show "Home" and not the rest, not exactly good.
The easiest way around this is to use static navigation. Update your custom master page with your own list for navigation, applying the proper class for whatnot for suckerfish and you get good to go. Problem is that you now have to update your master page each time you want to change your nav.
Next option is to use jquery to parse SharePoint’s rendering of your navigation, rebuild it in a suckerfish friendly way, and finally let suckerfish markup this. We have used this for quite a few customers because it’s quick and easy. You are throwing all of the heavy lifting to the client, and depending on how you build your html,css and js, there may be a flicker when the nav is being updated.
Third, the sledgehammer approach, hack the css and use jquery to add suckerfish like effects to your OOTB SP navigation. It is not the difficult although I do not find this elegent.
Fourth, create your own navigation web part that will render your sitemap in a way that you like. This would require knowledge of SharePoint and how to build a solid app. I would only recommend this for developers that are experienced with SharePoint.
I understand the desire to learn how to work with SharePoint, we all started with a request to branding SP for the first time from someone. The issue is that branding SharePoint is a very different skill than building a general site, modifying Joomla, WordPress, etc. You might find it much quicker to work with company that has the experience and knowledge of branding SharePoint so that it is done correctly. You could then use this knowledge for your next SP request.
I hope this helps.