How can I make my Google Apps domain to be OpenID provider. Is there any documentation, tutorial, working example something?
How to authenticate users in my own application using Google Apps domain authentication (I mean without OpenID). I've heard that it's something about gdata api but I don't know where to start. Are there any useful tutorials howtos or working examples?
I would like to know about free or open source solutions.
You don't have to do anything to make your Google Apps domain an openid provider. BUT, Google's special OpenID service for Apps for Domains requires OpenID relying parties to implement a special (proprietary) discovery mechanism and most RPs don't [yet]. So, if you're testing against that, it won't work.
One way to test is go to an OpenID RP that uses RPXNow. RPX is one of those RPs that do accept Google's new discovery mechanism. jyte.com for example. Try logging in there.