I want users of my service to be able to add their own custom domains. For example, www.[their domain].com should be able to access their application's index and show pages. My service is implemented in Rails 3.
I've seen apps like Tumblr offer this functionality for their front facing blogs. Although I have seen apps for Rails that implement sub domains in the way that Basecamp does, I have not found a resource for fully custom domains.
They'll need to create an A record in their DNS to point to your app servers IP. You'll need to know what domain they have pointed to your server and log it against their account, and also set your web servers config in such a way as to channel the requests from other domains to your app. You can then use the request object to look up their account in your application_controller.