PHP library for openID
The PHP OpenID library is good.
Which is the best PHP library for openID integration?
Integrate WebFinger, so you just have to offer an email input field.
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.
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.
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.