The obvious answer is that you have to make a serious effort to understand the matter from first principles. For mathematics, that would mean reading all of the definitions of all of the individual terms, and if any of those definitions are unfamiliar to you, looking them up in standard reference materials (such as textbooks) and recursively reading those definitions until you get to something you understand. Realistically, this is extremely time-consuming. You could spend months or even years trying to understand a single paper. Unfortunately, there does not appear to be a superior alternative.
An example. Several years ago, the renowned mathematician Shinichi Mochizuki publicly claimed to have proven the abc conjecture. It quickly became apparent, however, that he had basically invented an entire new branch of mathematics in order to do it. It took the broader mathematical community several years to evaluate all of this, eventually culminating in Peter Scholze and Jakob Stix writing a rebuttal to Mochizuki's proof, to which Mochizuki responded by claiming that they had misunderstood his argument. The proof was subsequently published in PRIMS, a mathematical journal of which Mochizuki is the chief editor (he was recused from peer review). The broader mathematical community still regards abc as a conjecture rather than a theorem, despite the published proof, because they feel that the proof is either incorrect, or at best, incomplete.
The point of this example is that the only way to find out whether something is nonsense or meaningful is to make a concerted and serious effort to engage with it. There are no shortcuts, even in perfectly objective contexts such as mathematics. If an amateur had presented this proof, it likely would have been rejected out of hand, but it just goes to show that people with credentials can still make bad (or at least, unconvincing) arguments. Conversely, people with limited or no credentials can make correct arguments whose correctness may not be immediately obvious. For example, Srinivasa Ramanujan developed a lot of important mathematical results despite a relatively modest education, but his arguments were highly unconventional and he had to contact several different western mathematicians before G. H. Hardy finally recognized his genius.