There are loads of documentation about that. Just google for "CSS", "Classes" and "background-color".
Basically you have to edit your style.css file and create a new class .featured (or so). Then you give the class a background-color, like this:
.featured {background-color: #ff0000;}
Then you need to edit your header.php file and find the code for the navigation bar. The class you just created needs to be assigned to the last list item.
<ul>
<li>list item 1</li>
<li>list item 2</li>
<li class="featured">last item</li>
</ul>
So yeah, that's basically how it works but when you have only little experience with css/html you should definitely read some tutorials first. Otherwise it can be a little frustrating...