You should just use OAuth2 and follow the recommended process by facebook. Have a look at the documentation of the facebook graph API here.
Remember to create a facebook developer account here.
If youre using ASP.NET, there is an included Facebook OAuth2 client. Have a look at this link here. Its actually pretty easy to accomplish a simple facebook login and retrieve an access-token.
I know thats alot of links but you will have to first read a bit about the whole process to understand how it works.
Hope this helps and good luck.