Moesif's guide explains how to integrate its behavioral email service with Mailgun to automatically send emails based on API usage, which can inform customers about technical issues or trigger business-related events. The integration process involves setting up an SMTP server using Mailgun credentials and configuring an email template in Moesif. This setup helps alleviate common email-sending issues like validation and spam identification by leveraging Mailgun's managed email services. The guide highlights the simplicity of the process and the benefit of keeping API consumers informed through automated communications, offering a 14-day free trial of Moesif's platform.