One of the most common questions My Artisan Web receives in our Support Tender is "How do I setup a Facebook Like Box in Joomla". You can do this easily with the tools provided in core Joomla without the need for downloading an extension for the job. To do this, you'll need to make use of the "Custom HTML" module option in the backend of your Joomla Administrative panel. You can create a custom HTML module and place the facebook code into the module to get a fabulous connection between the two.
To add a facebook like module follow these steps:
Go to http://www.google.com and type in facebook like box into a google search or go here: http://developers.facebook.com/docs/reference/plugins/like-box/