A little deeper dive on identity/authorization

During the ASP.NET Workshop we created a way to manage authorization and allowing people to log in. Wondering if we could go a little deeper into that?

Specifically I'm looking for examples where after a user has created an account on my site, I can then allow them to link that account to another service - or allow them to give rights to a 3rd party application to maybe hit APIs tied to that account.

Think of when you download an app like Tweetbot on your iPhone and it needs you to log in to your twitter account and authorize access.

Except in this case it would be I created a service called "EldorianService" and Jeff creates a mobile app that uses the EldorianService APIs, I'd want a user from EldorianService to give the authorization to link Jeff's mobile app to their EldorianService account.