Andrew Goodwin identifies 5 key areas for analyzing music videos: 1) examining the song's structure and vocals, 2) exploring the narrative and performers, 3) developing the star image, 4) relating visuals to the song, and 5) using technical aspects like camerawork, lighting, and editing. The music video should coherently tell a story that aligns with the song and increases with each viewing through the artist's narration and authentic performance that syncs with the music. Developing the star's image over multiple videos is also important for audience engagement.