The \"Likes\" plugin that I\'ve dropped on my page displays both the number of times the button has been directly clicked, as well as the number of times the page URL has be
I found two ways of doing this. The new way utilizing the graph api appears to be to be to use fql, as the following request shows:
https://graph.facebook.com/fql?q=SELECT url, normalized_url, share_count, like_count, comment_count, total_count, commentsbox_count, comments_fbid, click_count FROM link_stat WHERE url='http://mysite.com/8/the-dali-lama-returns'
The old way, with the Rest API which is in the process of being deprecated:
link.getStats()
https://developers.facebook.com/docs/reference/rest/links.getStats/
I know the post is old & not sure if you're only asking on how to incorporate the counter, but here are two things you can surely try.
SharedCount: You can check stats online as well as you can integrate their API. However, its free for approx. 10K API requests a month.
Edit: You can also see this question. https://wordpress.stackexchange.com/questions/133536/display-total-number-of-social-shares
TheBuzzz: You can test any URL online & returns total share counts from popular social media websites & also returns Moz Backlinks.
Hope this helps