You need a credit card, but as long as you don't use it "too much" you should be within the Free usage tier. You get 5GB, of storage, 2,000 PUT requests, 20,000 GET requests.
http://chartbeat.com/ is one option, Google Analytics now also has live analytics. You can get it all on one screen using a service like http://www.geckoboard.com/
You can track it server-side in the user's session or client-side (in-browser) with localStorage. If you do it locally, when they start record: window.localStorage.startAction = Date.now(); When ...
http://alanstorm.com/category/magento for programming tutorials. http://www.magentocommerce.com/wiki for general stuff.