Hi,
I think, tracking button clicks using google analytics, will require alot of customizations. What you can try, for an example, export your site as html and then open the site in html editor and then goto a link for which you want to track the click. You will need to enter the following code, (just for example, value are different depending on your site and code). Copy this snippet of code and use it on any of your hyperlinks:
<a href="" onclick="_gaq.push(['_trackEvent', 'Category', 'Action', 'Extra Label if you like!']);">Track my click</a>
Please check the complete tutorial by Google Analytics here
https://developers.google.com/analytics/devguides/collection/gajs/eventTrackerGuide
Hope this helps