To send emails through Twilio SendGrid's SMTP Relay using Node.js, you'll need to verify your sender identity and generate an API key. Then, install dependencies like dotenv and Nodemailer, store your API key in a .env file, and initialize Nodemailer with your API key. You can then use the transporter to send emails with a given message configuration, including headers for SendGrid features. After running the code, you'll see the SMTP response code being 250, indicating that the email has been successfully sent and delivered to the recipient.