How much about programming should I know in order to be a good game designer, and what would be a good language to learn for someone who has no prior experience in programming?
You don't have to know any programming language to be a noob designer, because designing is what it sounds like; you design levels and game play style. Although, in intermediate game design, it really helps to understand some programming to understand what a team can be able to pull off. For professional, it is a must; you would have to know both the limitations of the computers of the target audience and understand what kinds of strain certain level designs could have on a game engine.
I would recomend for a newb 2d designer, Game Maker
For 3d, I would recomend working with an already developed game and use their editor, like Half-life and the valve editor (which by the way is an excellent tool to start with because it is an additive editing enviornment, which can be much easier to manipulate, but can take hours to compile)