The best way is to be familiar with the historiography of the subject you're studying, and there's really no shortcut for that but to do the work. The historiography is the conversation that exists between historians about specific topics; Historian A back in the 40s wrote a book in which he argued X, Historian B in the 70s wrote a response and argued Y, Historian C in the 80s wrote a synthesis of the two while Historian D wrote a rejection of both and paved a new interpretation entirely.

All of these hypothetical historians are likely using the same set of primary sources, with some variance, but they're all likely asking slightly different questions about them that might not overlap. All of them will have strengths and weaknesses, and all of them will be subject to the author's analytical and theoretical framework. Historian A might be looking primarily at what Important Men were doing, while Historian D may have looked more at what "average" people experienced. Historian B was maybe looking entirely at structural factors like economics, social class, demographics and other concerns without delving much at all into personal experience.

You have to be able to see a secondary source as an expression of these parts before you can really ably start addressing its specific claims. Luckily, most historians just straight up tell you what their analytical and theoretical framework is, cite their sources directly, and tell you what question they're trying to answer and their proposed answer to that question. Usually, all of this is written baldly in the introduction, and then (usually) stated again in the conclusion. A historian wants their contribution to be a part of an ongoing conversation, and they do that by framing their work in the context of that conversation. Well-written academic books will, again, write this directly in their introduction, and will often write a brief overview of the historiography up to that point, articulating where it overlaps with others and where it departs.

Once you have all that in mind - and familiarity with those other works helps a lot - then you can start plumbing that source for its own sources and claims. If the book makes what seems like a weird assertion about a historical figure, and it still seems like a weird claim after reading all the other works in the historiography, then track it down: look for the nearest citation, read the citation, and try to get hold of the original statement. Is that ur-statement reliable? Where did that come from?

Sometimes historians make original claims that are based on their historical question, theoretical and analytical framework, and subject to a different set of research parameters. Sometimes the original content is defendable and adds a new angle on the question, and other times it isn't. The only way to really know which way it falls is to be broadly familiar with the conversation and to understand how historians structure their work in relation to others'. There's no shortcut.