Must I already have a foundation in calculus to smoothly get through it? What about linear algebra, or topology, or some other field of mathematics?
EDIT: I guess by "smoothly" I mean that you have enough knowledge that you won't have to go around consulting other sources in attempting to understand the book, and that nothing will be extraordinarily hard to grasp.
First of all you should specify what you mean by smoothly reading, I believe an interested senior in high school who is willing to work through the text and knows some basic algebra and trigonometry should be able to work through it.
However if by smoothly reading you mean you'll be able to get through any page in less than 10 minutes then you'll probably need to have already taken at least a couple of college calculus courses.