To receive an SMS message with C# and Twilio, developers need to install necessary libraries, extend their Controller with `TwilioController`, create an endpoint to accept POST requests with `From` and `Body` parameters, build a response in TwiML format, and connect their application to a Twilio number. The process involves using .NET MVC, handling Twilio's HTTP request, sending a customized response, and deploying the application to make it publicly accessible. With these steps, developers can receive SMS messages and interact with them programmatically.