To parse an incoming Twilio SMS webhook with Node.js, you can use Express and the Twilio library. The process involves setting up an Express server to receive incoming messages, installing necessary libraries, and configuring your Twilio account. Once set up, you can access information about the incoming message, such as its body and sender number, using the `req.body` object. This information can be used to make decisions based on the content of the message or the country it was sent from. The example code provides a basic starting point for building an Express server to receive Twilio SMS messages and respond with another text message.