To programmatically download an image from an MMS message sent to a Twilio number, developers can use Node.js and the Twilio MMS library. The process involves creating an Express app that receives HTTP requests from Twilio when a text message is sent to the designated phone number. The app then uses the `request` module to download the images contained in the message and save them locally. To test this setup, developers need to create a Twilio account, buy a phone number, install the necessary dependencies, and use tools like ngrok to expose their local app to the public internet. This setup enables developers to receive images via text messages from users and can be used as a starting point for larger projects that involve image manipulation or processing.