Using Google federated login with Google Apps and ASP.net application

As an organisation, we use Google Apps. We have the paid version (mapped to our domain) etc...

We are developing a web based application to manage orders, and other business functionality. I want to be able to use federated login with our google apps accounts- For example, if a user is logged in to their email (gMail) - they should automatically be logged in to our ASP.net application If they're not logged in - the log in form should auth. against our google apps account.

How can this be done? Is it possible to be able to "get" the user who is currently logged in using this method etc...?

Sure, use dotNetOpenAuth. It's recommended by OpenId library and it should be easy in use. As far as google provides OpenId interface there should be no problem with using it in your application.

Stackoverflow is successfully using it and I'm logged here always when I'm logged on my google account.

Just doing a quick search through Google's API documentation, it sounds like you need to use Google's implementation of OAuth protocol.

If you have not yet started developing, you could even considering developing for Appengine - using python or Java (though I would prefer Python myself).

Advantage is that it has a much closer integration with Google Apps services and it will be much easier to build further functionality that works with Google apps (docs/mail etc). Besides this, there arent too many hassles for hosting the app.