I have an element that already has a class:
Just to elaborate on what others have said, multiple CSS classes are combined in a single string, delimited by spaces. Thus, if you wanted to hard-code it, it would simply look like this:
From there you can easily derive the javascript necessary to add a new class... just append a space followed by the new class to the element's className property. Knowing this, you can also write a function to remove a class later should the need arise.