The common image that I've seen to describe the 'everything's expanding from everywhere' is to think of your 2D surface as being the skin of a perfectly elastic balloon. When you inflate the balloon, all the little Flatlanders on the surface perceive the inflation as their universe expanding - but the center of the expansion always seems to be the point where the observation is being made. The actual center of expansion is out in the third dimension. Let D=D+1 and things get trippy.
Since I suspect that many people here might be interested: Rudy Rucker (also known for his 'Wetware' cyberpunk series) has made the contents of his book
The Fourth Dimension available as a
free webpage. I discovered this book in college, but the language really makes it accessible to anyone old enough to make a forum account