To deploy a Twilio webhook server on Replit, a developer-friendly hosting platform with a free tier, follow these steps: create a new project, install the Twilio library using poetry or pip, copy and paste a Python webhook server code into the main.py file, start the web server by clicking the "Run" button, buy a Twilio phone number, configure the webhook URL in the Twilio Console, and test the bot. To secure the webhook for production use, replace the Flask development web server with Gunicorn, comment out the interpreter configuration section in the .replit file, and restart the project. With this tutorial, users can deploy their Twilio webhooks on Replit and learn about security measures to ensure legitimate calls originate from Twilio.