In Rails 4 PATCH is the new HTTP methode for an update action. You can find the details here: http://weblog.rubyonrails.org/2012/2/25/edge-rails-patch-is-the-new-primary-http-method-for-updates/
As you can imagine you need to use the PATCH method to test the update action in your controller. Because of how the users controller in this example works you need to specify the id and user. This particular spec tests whether the user gets redirected if it's not logged in.
(./spec/controllers/users_controller_spec.rb)
require 'spec_helper'