You can use the CSS class selector to fetch the element. The class selector works like this:
$('.name_of_class')
This then returns a jQuery object of that DOM element, on which you can call various methods to do various things, such as animation, content manipulation and really anything that you can do with jQuery.
In your example here, you can fetch the innerHTML value (the element's content) by calling:
var content = $('.leftpanel_keywords').html();
There are plenty of places to read more about jQuery selectors, DOM traversing and DOM manipulation, some of the most vital parts of jQuery and basic building blocks for exciting functionality! Check out jQuery for Designers, a great collection of simple, hands on tutorials and screencasts. Also look at the jQuery official documentation, which is a comprehensive reference.
Hope this helps!