To view Twilio SMS notifications on your desktop with Python and FastAPI, you need to set up a virtual environment, install required modules, create a FastAPI application, run the server, and start ngrok. The ngrok URL will be used to configure a webhook on your Twilio phone number. When an SMS is received on your Twilio number, the notification application will receive a request to the /notify endpoint, creating a desktop notification with the details about the SMS message you received.