Alright, let's dive in! First things first, you'll need to get into your Supabase account. If you haven't already, create a Supabase project. The official Supabase docs are super helpful for this. Just follow along to set up your new project.

Next up, Twilio! If you don't have an account yet, go ahead and register. Once you're in, grab your "ACCOUNT SID" and "AUTH TOKEN" from the dashboard. These are like your keys to the kingdom. Head over to the "Phone Numbers" section and either buy a new number or use one you already have. Jot down that number; you'll need it soon.

Now, let's get into the nitty-gritty. Create a new .js file in the pages/api directory of your Supabase project. You can do this with the command touch pages/api/sms.js. This file will handle sending SMS notifications.

In your new sms.js file, import Twilio from the twilio library and initialize it with the credentials you got from Twilio. Your code should look something like this:

const twilio = require('twilio');
const client = twilio(process.env.TWILIO_ACCOUNT_SID, process.env.TWILIO_AUTH_TOKEN);
the api consists of both message body and the recipient phone number. 

Time to create the function that sends the SMS. This function will take an input object with the message body and the recipient's phone number. Here's a simple version:

async function sendSMS({ body, to }) {
await client.messages.create({
      body,
      from: process.env.TWILIO_PHONE_NUMBER,
      to,
    });
}

Don't forget to replace process.env.TWILIO_PHONE_NUMBER with the Twilio phone number you noted earlier.

Now, whenever your app needs to send an SMS, just call the sms.js API you created in your Supabase project with the necessary parameters. Twilio will handle sending the SMS, and any responses will come back to your app through the API you set up.

Make sure to check all the API responses and add error handling. Twilio might throw errors for things like invalid phone numbers or low account balance. Always test thoroughly before going live.