Conect unity game and website using facebook API

Hi! I am working on a project that involves a bunch of games and a website for them. You can login to the website giving a username; password. You can type your login information in the game, the game sends them via $_POST to the website, which (if the information is correct) sends back some information from your account. Now I want to add the option to log-in woth facebook. The website is ready and it works well. You can register/login with facebook. I have downloaded the unity facebook plugin too, which works as well. I have created a facebook app which I connected with the website and the game as well. Now I am looking for a way to login with facebook in the game and download the neccessary information from my account without having to type username and password. How could I do it? Thank you for any answers in advance!