The rabbit hole goes all the way down, because economics is very far from a solved problem, and even in the rare case where the economics is entirely unambiguous, the application to historical cases is surely not. But for an overview of what economic history does, and the kind of thinking used, try Robert (Bob) Allen's Global Economic History: A Very Short Introduction.

If you want the kind of economics necessary to understand history generally, you probably want to start by acquiring a generalist's economic perspective, rather than detailed study of any one discipline. This is the sort of thing one picks up reading The Economist, which, for all its faults, is still a pretty good place to get economics-informed analysis of present-day situations written in generally plain language. This is a good enough starting point for using economic tools to understand social situations. Of course, have to be careful to understand that this is only an entry, and the past it its own territory. You may need slightly or even radically different toolkits to understand how its economies worked, and for that, you'll almost certainly need to read economic histories of the relevant times and places. There are very few absolute rules, and the details frequently matter a great deal. But if you don't start somewhere, then you don't start anywhere.