To build a simple chat app using JavaScript, Node.js and Twilio, start by creating a Twilio Chat Service in the console, setting up an API key and secret, and cloning a GitHub repository that provides a starter codebase. The backend code is written in server.js, which uses the Twilio library to generate an access token for users based on their identity. This token is used by the Twilio client SDK to interact with the Chat Service. Meanwhile, the frontend code references scripts and styles from the Twilio Chat client SDK, including a micro-template for chat messages.