Secondarily, are there strategies for doing this that can be generalized to many fields? Or does each field require its own strategy?
The answer is almost always to start with the basics. Trying to shortcut past the introductory level topics and skip straight to the hard stuff results in a lot of pseudoscience and false understandings.
Realistically, no one is going to understand cutting edge neuroscience or quantum mechanics by reading pop-science articles. If something looks interesting, pick introductory texts in that field and start working your way up.
My question means to ask how someone can intellectually pull themselves up by their bootstraps. I guess starting with basics may be one way of doing that.
A layperson can get themselves to the level of a college student who has taken intro courses with the right textbook + online resources if they are passionate. Wikipedia is actually quite good for looking up technical concepts. You must work example problems. Having intuitive understanding of key concepts in the field, and having practice applying them quantitatively to simple problems is necessary for further progress.
Once you are at that stage, the loop will involve reading materials where you understand maybe 70-90% of what is going on, and looking up new concepts as you go. Wikipedia and textbooks will still serve you well as you reach intermediate/advanced undergrad level. Focus on forming connections between things you have studied using the key concepts in the discipline. You must still do lots of targeted example problems.
The next stage involves narrowing the scope. There is no way to be on all the bleeding edges at once. Sign up for a membership in a relevant professional organization (ACM, APS, and so on) which will usually get you some kind of nice periodical delivered to you monthly with well-written articles especially for people practicing that highlight new developments (for physics check out physics today, for example). These articles will be highly accurate and communicative yet still written for a non-specialized audience. They will be a goldmine of inspiration for what to dive further into, and will teach you alot in an efficient manner.
Now you are near the bleeding edge. You may need access to proper library resources with the necessary journal/database subscriptions depending on your field (i.e. Chemistry). For physics the arXiv is great but isn't everything, especially for older stuff. Follow up on journal article references. If you are feeling swamped, look for a "review article" which is basically designed to help people in your situation get up to speed on a topic. The introductory sections of PhD theses can also be broad yet digestible, and they are often freely available online. Wikipedia will either have nothing, or will have highly technical entries possibly written by the same authors as the papers.
You will start to recognize authors as you read more on a certain topic. You will start to notice people's students/collaborators moving elsewhere and starting their own related research as you look through the timeline. At this point you might have specific questions for these people, so you might email them or even attend/stream a conference where they are presenting.