How to add a class to an element using jQuery and javascript?

How to add a class to an element using jQuery and javascript?

I have the HTML code as given below to add the navigation to my site.
(Note that the list is nested)
<div id="navigation">
<ul>
<li><a href="default.html">Home</a></li>
<li><a href="about.html">About us</a></li>
<li><a href="help.html">Help</a></li>
<li><a href="#">DropDown</a>
<ul>
<li><a href="#">Link 1</a></li>
<li><a href="#">Link 2</a></li>
<li><a href="#">Link 3</a></li>
</ul>
</li>
<li class="last"><a href="#">A Last Link Text</a></li>
</ul>
</div>
I want to show the currently active page link in new color. So the
corresponding list item should have the class active and I use the CSS to
change the color. For example, if the default.html is the currently opened
page, the code should be <li class="active"><a
href="default.html">Home</a></li>.
How to do that in jQuery and JavaScript (I need both for two different
websites). Can anyone help me?
Thanks for your help.