To send an SMS from a Svelte app, it's necessary to create a backend API using Twilio Functions, which provides a serverless environment for deploying backend services without exposing Twilio credentials. A new Function Service is created with a path name /sms, where a shell function code is written to handle the request. The function sends an SMS using the Twilio Node.js REST Client and returns a response with a success message or an error. After creating the API, a Svelte app is scaffolded with a button that makes a POST request to the API when clicked, sending a message and updating the UI with a success status.