Dombrovskyi, have you created an API Key and Secret? If not, I think you need to start with that:
http://facebook.com/developers
create a name for your "app" ie. website name
You will then see the key and secrete to use within Joomla
I think you need to enter the key in the Social API field within the Template settings. I've also entered the key and secret within the Authentication - Facebook Plugin.
Again, I'm not really sure if I'm doing this correct and I'm still having an issue. Now when I try to login with FB I'm getting the following message:
An error occurred with Californiastandup.com. Please try again later.
API Error Code: 191
API Error Description: The specified URL is not owned by the application
Error Message: redirect_uri is not owned by the application.
Hope someone can chime in and provide some direction. Good luck.