Reddit mentions of The Fundamentals of Political Science Research

I'm a Political Methodologist; I'm happy to give you some help. It would be useful to know what your mathematical background is, and what sort of things you're interested in doing. You have to understand, to me, this question is a little bit like "I'm interested in American Politics; suggest an introductory text, please." There's a huge variety of stuff going on here, it's hard to know where to start.

Do you want to be able to read statistics wrt PoliSci? Or are you interested in figuring out how everything works, so that you can create / replicate?

If you want something very undergraduate centric, my undergrad research methods class used the Kellstedt and Whitten book. It was fine, but obviously very rudimentary. It will get you to understand some of the big picture type stuff, as well as some of the simple statistical nuts and bolts you'd want to understand. This class also used the everpresent King, Keohane and Verba text, which is oriented around qualitative work, but Gary King is the foremost quantitative methodologist in the discipline, so it's still pretty good (and "qualitative" certainly doesn't mean "non-rigorous" -- it's cited a lot because it really delves into deeply into research design). That said, I don't remember a whole lot about this class anymore, and I haven't looked in these books for ages. My feeling is that both of these books will probably be close to what you're looking for -- they're oriented around intuition and identifying the main issues in inference in the social sciences, without getting too bogged down in all of the math.

That said, if you have more math background, I'd suggest Mostly Harmless Econometrics which is often used as a first year graduate level quant methods book. It's absolutely fantastic, but it isn't easy if you don't have the math background. It may also assume some preexisting rudimentary probability or statistical knowledge. I'd also suggest the Morgan and Winship. These two books are structured more around causal inference, which is a subtle reframing of the whole "statistics in the social sciences".

For more nuts and bolts econometrics, Baby Wooldridge is one of the standards. I think it's pretty often used in undergrad econ classes.

In general, though, statistics is statistics, so if you want to learn it, find an appropriate level of statistics/econometrics book.

Take a look at those books in your library/online/etc and see if any of them are what you're looking for.