The author of the text views evangelizing quality as sharing knowledge and expertise to improve quality, rather than a traditional preaching approach. They suggest that negative experiences can trigger a focus on quality, and provide various methods to get people to think more about it, such as customer feedback, metrics, retrospectives, being vocal, competitive, and part of the solution. The author highlights two key factors in improving quality: small user stories and developing to the test. They emphasize that building a culture of quality and sharing ideas through writing, emailing, or talking to others can lead to change and improvement.