PHP library for openID
The PHP OpenID library is good.
Which is the best PHP library for openID integration?
OpenID for dummies?
Some more selectors:
My personal favorite is openid-realselector (demo).
how to implement php login or authentication session
The Zend framework is good if you want to have a lot of pre-buildt libraries, but be free to mix and match with your own or third-party. The Zend framework includes Zend_Auth, which is complete and ready for use.
Integrate WebFinger, so you just have to offer an email input field.
There is an easier way. JanRain offers OpenID (and facebook) as a service http://rpxnow.com . Vastly easier/quicker than going native with the libraries.
This question might be "old", but the question ranks quite high on search / google and is still highly relevant, so i would like to add my answer:
As a login is probably the most important thing in your app, you should use something that is secure, up-to-date and stable. I would like to promote https://github.com/panique/php-login or http://www.php-login.net (same!), which is my project. It's the most starred, most forked and most discussed php login script on github, it's highly maintained and a lot of good php people have looked over the code.
If you want to build a script from scratch, you should use the PHP 5.5. password functions! They are highly secure and future-proof, made by experts. I made a wiki page on how to handle those functions here.