To forward incoming SMS messages from Twilio to an email inbox using Gmail, you need to have a Twilio account with SMS capabilities and a Gmail account. First, create a Twilio phone number and set up an app password on your Gmail account. Then, create a Twilio Function Service with environment variables for your Gmail address and app password. Add the necessary dependencies and create a function that uses nodemailer to send emails from the received SMS messages. Deploy the function and configure your Twilio number to handle incoming SMS, then start sending test SMS messages to forward them to your email inbox.