Consider this simple example: getk2.org has around 20 links that rarely change. I wanted to know how many people download K2 from this particular website (and not some third party source), how many people click on the documentation, how many get the SVN version of K2 and so on...
Having read the manual over at GA help, I came down to some basic event tracking usage with GA on getk2.org. The goal was to see for the first time how users "behave" inside getk2.org and not just how many come in. GA event tracking organizes results in this manner: Categories, actions, labels. That translates to specific "pages" (or some entire section in your site, e.g. Sports news), things that we anticipate users to do (e.g. click on a link or download a file) and finally, names of the actual links being clicked (e.g. "K2 main file download"). If you're not lost, bare with me for a sec...
First off, I only wanted to track the K2 homepage (getk2.org) so I used 1 "category" in my events: "K2 Homepage"
Secondly, I divided my anticipated "behaviors" (the "actions" in GA lingo) into just 2: visit (for links) and download (for file downloads).
Thirdly, I labeled all links to be tracked in a way that makes sense to me... So the K2 download button is labelled as "Stable release". I don't need to mark it as "Stable release download", because I've already assigned to that link the right "action" (Download).
So I prepare these "onclick" JS events, to add them into my homepage links... well, the most important ones... And I let GA track those event for around 2 monts...
To give you an example of such an event:
<a href="http://domain.com/about.html" onClick="_gaq.push(['_trackEvent', 'My homepage', 'Visit', 'About Us']);">About Us</a>
Now I come back to GA and go (on the left sidebar) to Content >> Event Tracking and I can see how my visitors behaved... Well, here's a surprise! I didn't know so many people where downloading the SVN release! Needless to say, the results where very encouraging! I won't go into detail, but it's worth trying this on your own.
If you want a solution that hooks up GA tracking events in Joomla, I can't say I know any specific... If you do, please let everyone know in the comments.
But it should not be difficult to implement these events, e.g. in K2 attachment downloads or in other components... Maybe a plugin could also attach such events using JS automatically onto any link that is a file (e.g. PDF, ODF etc.). Or a combination of JS and Joomla PHP to use e.g. the "title" of the link to create the "label", the file extension in links to determine the "action" and the current page (by Joomla) to assign the "Category".
I hope you enjoyed this small introduction into GA tracking events. You can see how to attach these events by examining the source code in: http://getk2.org