What specific tasks will a video game designer need to perform

Depends on your specific field. There is no class for video game designers. Artists create the textures that make up the world, programmers create the code that makes everything happen in the game. Storyboard members develop the narrative and composers develop the music. However, its not that simple, for if none of these experts communicated and bounced idea off one another then you could very well come up with a game with a serene artistic feel but have mechanics of a shooter game while the music was rockin' deth metal.
In short, while what you majorly do as a video game developer depends on your specialty, to be of any use in the industry today, you must be fluent in both art, and code. narratives, and symphonies. You must be cultured in everything even in your competition, I can guarantee there are at least a few copies of black ops in the Bungie studio, and vice versa.

So immerse yourself in every aspect of the game, not just the bit thats in your job description