How to integrate Facebook into WordPress registration/login?
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/
Facebook supports OpenID.
There is an OpenId plugin for Wordpress I know nothing about.
The best plugin which integrates Facebook (and also Twitter and Google Plus) is WordPress Social Login.