I have taken up to and including introduction to real analysis and introduction to partial differential equations.  I just barely passed those.  If that's not enough, what would I have to study to understand that book?

Also, how clear is it?  I've had a lot of trouble with math/stats textbooks that say things in the first introduction to new topics "If given premise A, one can quickly and easily see that conclusion Z flows from it" while leaving out steps B to Y.

Regardless, I will definitely take a closer look.  Thanks.

It depends a lot on what sort of stats problems you're doing and what sort of data sets you're working with. Generally, and you might not like this, you'd get a practical exposure to "working with real data" in whatever field you're working at in upper-level courses in your field (depending on your field, that will either mean upper-level undergraduate or beginning post-graduate). If you can't actually do it in the field like that, what might be your best bet is to read papers (ugh) where you can get the raw data and run your own analysis of it, trying to replicate what they did (ugh).

Otherwise, there's a terribly practical guide to doing this stuff with social sciences data called The Logic of Causal Order by James Davis. He runs NORC and I had a class with him. He wears bow ties and suspenders. The monograph really helps you think about how you must run your regression analysis, and the thinking part is the most important of them all.

I have this same problem, in that I have a minimal statistical education and a very strong maths education, and people sometimes want me to do statistical analysis of crap here because I'm the only person resembling a statistician for miles. I mostly figure it out.