How to integrate Facebook into WordPress registration/login?

Solution:

After several trials, the best plugin for this kind of job is http://wordpress.org/extend/plugins/social-connect/ It covers not only Facebook but also Twitter, WordPress.com and Google

Here you can find some details on installing it http://giannopoulos.net/2011/12/28/how-to-add-facebooktwitteretc-authentication-on-wordpress/