[bluenose69]

This is not easy to do, even for experts. An expert will often take several days to do a peer review of a paper. It's not really possible to review papers outside a narrow field of expertise, partly because doing so requires being well-read in the relevant literature, and knowing which groups are working on what topics, what methodologies are showing promise, and so forth.

And peer review does not get to the question of whether things are "legit". Likely you are quite aware of problem cases that come up in the news every once in a while. Bear in mind that those problem cases were peer reviewed, often through many, many stages, and nobody twigged to the problem.

Perhaps the answer to "what" question is: get an advanced degree, work for a decade or so in a particular sub-field, attend conferences to know what is being done at the cutting edge, spend a lot of time reading, and use all the tools at your disposal to evaluate the work.

In a nutshell, I'd say that non-experts should not expect to be able to evaluate the legitimacy of scientific papers and experiments. And even a highly-skilled expert in one sub-field is a non-expert in another.

There is no simple N-step program to yield what seems to be sought in your question.