Building a chatbot with OpenAI's GPT-3 engine, Twilio SMS, and Python involves several steps. First, a separate directory for the project is created, and a virtual environment is set up using Python 3.6 or newer. The OpenAI API key is obtained by requesting beta access, and the necessary packages are installed using pip. A Flask application with a webhook definition is created to receive incoming SMS messages and generate responses. The chatbot's ask() function is used to send user messages to the GPT-3 engine and maintain the chat log in the session variable from Flask. The Flask application is run, and ngrok is used to provide a temporary public URL for the chatbot to be accessible over the internet. With the Flask application and ngrok running, users can start sending SMS to the chatbot with their first question, and the bot will respond accordingly.