I will integrate Facebooklogin into your web site. Please see how i achieve my this job:
Create App on F.B
Integrate the App with your site.
Do all App Settings
Live the App
PROCESS: When user come to our site. if you have login or registration option. you just put the login button there. Users click on the login button and they will redirected to FBlogin screen. when they put their login details. The App ask for permissions. After Facebook permission the URL redirected directly to our website. Where we can store the USER INFORMATION what we required for our website/Application.
With this way we can achieve our FBlogin.
Please order me if you need everything in professional way.