Elgg 1.8.x Facebook Connect Plugin provides you log in and registration with Facebook. For enable this feature you must create Facebook Application for App Id and Secret code.
Lets see How to create your first Facebook Application.
A Facebook Account with Developer Application Enabled (mostly It comes with).
Go to http://developers.facebook.com/ and log in with facebook email and password.
You will get facebook App Id and Secret Code here you can choose Category and Sub-category according your website.
Click on Save Changes and You are all set.
Now note down App Id and Secret Code and login your site with Admin, go to Settings then Facebook Connect Setting(make sure you have activated facebook connect plugin), find Facebook Application Id and Facebook Application Secret Code edit them enter your facebook app Id and secret code here and Save them.
Here you will find other setting options.