Ruby on Rails Web Application to iOS or Android app?
I understand the question is about Ruby on Rails to iOS/Andriod. Have you considered from Ruby to iOS/Andriod? Have a look at RubyMotion. I think its easier with RubyMotion to connect mobile app iOS/Andriod with the Ruby application rather than via web application ROR.
It will take a lot of reading.
You will need to build an API on rails framework to communicate with an mobile application. Here are some good links for creating an API with rails:
http://railscasts.com/episodes/350-rest-api-versioning http://collectiveidea.com/blog/archives/2013/06/13/building-awesome-rails-apis-part-1/
I would suggest using Devise for authentication and using their authentication_token to validate users network requests to your API.
http://matteomelani.wordpress.com/2011/10/17/authentication-for-mobile-devices/
Here are some helpful links that I bookmarked awhile ago to help.
http://pnhoang.tumblr.com/post/24160454924/build-a-rails-backend-api-for-an-iphone-client http://www.takeofflabs.com/posts/8-Rails-and-iOS-a-sample-starting-setup https://devcenter.heroku.com/articles/ios-photo-sharing-geo-location-service http://jessewolgamott.com/blog/2012/01/19/the-one-with-a-json-api-login-using-devise/
Best of luck