In the default config/routes.rb file you will find the following comment quite a long way down:

# You can have the root of your site routed with "root"
# root 'welcome#index' 

If you comment out the last line there, you can define your http://0.0.0.0:3000/ with it. Let's put it on home#index:

Shop::Application.routes.draw do
  get "home/index"

  get "home/ping"

  get "home/pong"

  root 'home#index'
end

Our new routes:

$ rake routes
    Prefix Verb URI Pattern           Controller#Action
home_index GET /home/index(.:format) home#index
 home_ping GET /home/ping(.:format)  home#ping
 home_pong GET /home/pong(.:format)  home#pong
      root GET /                     home#index
$

If we go to the root URL http://0.0.0.0:3000 we now see home#index.