Something to look at is articles or blogposts where someone is dissecting studies and showing their working. An excellent example is Scott Alexander’s assessment of studies of ivermectin for Covid.

I wrote a post summarizing misuses of statistics here. You can read that if you want a short version. If you want to learn to evaluate studies and gauge their rigor, then read Inuitive biostatistics by Harvey Motuslsky and Statistics done wrong by Alex Reinhart. These were my main sources for my post. After reading them you should have a good understanding of statistics intuitively, without necessarily knowing the math. If you have to read only one, then definitely go for Intuitive biostatistics. It includes perhaps 90% of the content of the other book and more, because Statistics done wrong assumes you've taken at least an introductory class in statistics, but Intuitive biostatistics doesn't. Read it at your own pace, take time to understand every point, especially the "common mistakes" parts. Don't speed-read the book, understanding statistics will improve your critical thinking more than reading 100 other books, so don't worry if it takes time. If you don't understand the explanations for the "common mistakes" then check out Wikipedia or the explanation in Statistics done wrong. If you prefer online courses to books then you can take an introductory statistics MOOC and then read Statistics done wrong, which is shorter than Intuitive biostatistics. Good luck !