To verify users on WhatsApp with Python and Twilio, first create a Twilio Verify service and set up a Flask application. The application will send a verification code to the user's phone number via WhatsApp after they enter their phone number. The user can then enter the verification code on the application's website to receive a success message. The application uses session storage to store the user's phone number, which is deleted once the verification is successful. The Twilio Verify service sends the verification code and checks its status when it is submitted by the user. If the code is correct, the user is redirected to a success page; otherwise, they are offered another chance to enter the code.