To send a WhatsApp message using the Twilio API, developers can follow the step-by-step process outlined in this tutorial. The process begins by setting up a new .NET Core application and adding the Twilio NuGet package, then initializing the Twilio REST client with an Account SID and Auth Token. Next, developers need to call the MessageResource.Create method, passing in the sender's and recipient's WhatsApp numbers and a message body. After building and running the project, the code can be restored to ensure all packages are downloaded, and the application can be run again. The tutorial concludes by encouraging readers to progress to integrating their new application into existing projects and exploring additional resources for more ideas and tips.