Facebook gives you a way to track “likes” and “Shares” from content on your site.  It’s called “Insights”.  To use it, just go to:

www.facebook.com/insights

The first think you have to do is “claim” your domain, which means to tie your domain to your facebook account.  Facebook gives you a meta tag to add to your home page.

If you have problems claiming your domain try “DeLinting” your site by going here:

http://developers.facebook.com/tools/lint/

Note you must be logged into facebook to do this.  Type in your domain name, and click the “Lint” button.  That may help you get going.