I am wondering how it is possible to get information from link clicks.
For example, a user is logged in and clicks a link. Is it possible to record that information? Number of links clicked, which ones, etc... things like that.
I have no idea how to do this. Any ideas / links to information?
You could use JavaScript to bind an event to your links and have the logging done that way. See this question.
You also might try looking at setting up Google Analytics on your site; it's a free service that offers incredible amounts of data collecting for your site. Here's a blog post that details tracking clicks with Google Analytics.