To build a WhatsApp chatbot with Ruby, Sinatra, and Twilio, start by setting up a new Ruby application, installing necessary gems, and configuring the Twilio API for WhatsApp. Create a webhook route to handle incoming messages, parse the message body, and respond with TwiML using the twilio-ruby library. Use APIs to retrieve dog or cat facts and pictures based on user input. Secure the webhook by validating the request signature using the Twilio auth token and rack middleware. Finally, test the bot by sending a message to the WhatsApp sandbox number and configure the ngrok tunnel to direct incoming messages to the application.