With Twilio's Messaging API, users can programmatically send WhatsApp messages using Python. To start, a developer needs to set up their development environment by installing the required software and creating a free Twilio account with an activated WhatsApp Sandbox. The sandbox allows for prototype messaging without waiting for a dedicated number to be approved by WhatsApp. Once the sandbox is activated, developers can use it to send WhatsApp messages using Python code, which requires installing the Twilio Python library and setting environment variables for the Twilio account credentials. The code snippet provided demonstrates how to create a simple WhatsApp media message using a pre-approved template and a shared phone number from the Sandbox.