To send SMS notifications with CakePHP and Twilio Notify, start by creating a new CakePHP application and configuring the database connection. Then, migrate the users table and add the Twilio PHP SDK to your app. Next, set up user registration using the bake console and configure password hashing for security. After that, create a Notify behavior class within CakePHP using the bake console, which will interact with the Twilio API to send SMS notifications. Implement the notify behavior in the Users table by adding it as a behavior and binding users to the service. Finally, test your app by navigating to the registration page and creating a user account with a phone number; on successful registration, you should receive a welcome message.