A developer can use Segment to track website or app usage and send corresponding SMS notifications whenever a button is clicked on the site. To achieve this, you need to add a Segment source for your website, set up an HTML file with a button click event that calls the `analytics.track()` function, and create a Twilio Function using Serverless Toolkit to send an SMS notification when the button is clicked. The Twilio Function is then connected to the Segment console as a Destination, allowing it to receive alerts when the site has been visited or a button has been clicked.