To build a voicemail system with Twilio and Ruby, start by setting up a new Rails project, installing the necessary gems, and configuring the environment variables. Create an initializer for the Twilio client and define routes for answering incoming calls, handling unanswered calls, and recording messages. The `initial_answer` method returns TwiML to answer the call and redirect it to your cell phone number, while the `handle_unanswered_call` method plays a message and starts recording if the line is busy or the caller doesn't answer. The `recordings` method sends an SMS notification with a link to listen to the recorded message after it's finished. To serve the application publicly, use ngrok to create a tunnel to your localhost server and configure the Twilio phone number to call the `/initial-answer` endpoint when there is an incoming call.