The author, Phil Nash, explores how to build a Twilio application with Rails 5, starting by installing Rails 5 and creating a new application using `rails new`. They then add the `twilio-ruby` gem and create a controller for handling incoming calls from Twilio. The controller uses Rack middleware to verify requests coming from Twilio and responds with TwiML instructions to play a message or send an SMS. To make the app accessible over the internet, ngrok is used to tunnel the local server's port 3000 to a publicly accessible URL. With this setup, Twilio can route incoming calls to the application, which then responds with pre-defined TwiML instructions.