To build a video calling app using Flutter, developers need to follow five steps: first, integrate the Video SDK into their app, setting up permissions and configurations for Android and iOS; then, create a join screen where users can create or join rooms, followed by creating room controls with buttons to leave, toggle mic, and toggle camera; next, develop a participant tile widget to display remote participants' video streams; after that, create a room screen that manages the room's state and updates in real-time; finally, modify the main app file to conditionally render either the join screen or room screen based on whether a room is active.