To enable video calls for a demo Next.js application using Vonage Video API, you need to clone the existing application code from a GitHub repository and prepare the necessary prerequisites such as Node.js environment with version 12.8 or above, git command line environment, an account on the Vonage Video Platform, and an account on the Vonage Developer Dashboard. You then create a new project in the Vonage Video Account page, copy the iframe-generated code, and add it to the data directory. The application uses the iframe option to enable video call functionality. To send SMS notifications, you need to provide environment variables such as VONAGE_SMS_BRAND, THERAPIST_PHONE_NUMBER, and VONAGE_API_KEY. After installing dependencies and running the server, you can access the application at http://localhost:3000 and schedule a video call with a therapist. The application uses Next.js framework for building full-stack web applications on top of React library, providing features and conventions that allow developers to build applications quickly with excellent developer experience.