To send Twilio SMS messages using Python on Google App Engine, one can follow a step-by-step guide that sets up the environment and writes all necessary Python code to send a text message with a random quote from Jack Handey. The process involves setting up Google App Engine, installing required libraries, authenticating with Twilio, and sending an SMS message. This tutorial is part of a larger set of resources available on the Twilio website, including documentation, sample apps, and developer community hubs.