To send an SMS text message via the Twilio REST API with PHP, one can follow a five-step process that involves downloading the Twilio PHP Helper Library from GitHub, setting up account credentials and message data, and then posting to the API to send the message. The example uses the Twilio PHP Library available on GitHub and includes additional resources such as an SMS Alerts and Notifications HowTo and a Resource Center with ebooks, industry reports, and webinars. The process is designed to be easy and straightforward, making it accessible to developers of various skill levels.