To receive and respond to text messages with Hanami and Twilio, developers need to install the necessary gems, create a new Hanami project, generate an app for webhooks, configure it to return XML responses, and write an action to handle incoming SMS messages. The action can be generated using a generator, but also requires writing code to bypass templates and views if desired. Once the action is in place, the application can be connected to a Twilio phone number using ngrok, and tests can be written to verify its functionality. Throughout this process, developers will learn about Hanami's architecture, its ability to accommodate different apps with varying configurations, and its flexibility in separating concerns and bypassing unnecessary objects.