For now, I'm a Ph.D. student in CS with a very specific subarea, but I'll do my best to suggest approaches that I think are useful for general scientific inquiry.
>Where and how to find papers
There's a couple of approaches here, based on how specific your knowledge/interest in the field is.
mentioned, Google Scholar is an exceptional resource for finding papers for a specific topic (for example, "statistical methods used for scoring coreference agreement"). It's also pretty nice for following citation chains, IIRC.
Otherwise, many people post topics to arXiv.org, tagged with the relevant areas. IIRC, arXiv can email you about new papers in a field you're interested in, or there's a reader that aggregates them, or something like that, so it's helpful for keeping up-to-date as well.
I also suggest finding out what conferences and journals are relevant to your interests and reading what's published in those. Some of these are, of course, paywalled, but it's usually not too hard to find an alternative source (I know plenty of authors pre-publish to arXiv, or will post a non-print copy to their own webpage). I should note that you should look for various signs of the health of a venue: high citation count is one metric, but reading what people in the field think online is also important; basically, look for the conferences and journals that are respected in the field.
>How to read them
Follow these steps, and if at any point it seems too irrelevant, set the paper aside:
1. Read the title
2. Read the abstract
3. Read all the section headings
4. Read the introduction
5. Read the conclusion
6. Read the first sentence of each section
7. Read the first sentence of each paragraph
8. Read the rest of the damn paper.
This is an iterative approach that abuses good writing habits by reading the higher level information first, so you can opt out quickly and not waste your time.
Unfortunately, I don't have any pro strats for digging into the meat of a paper other than to read it and try to work through what they're saying to really understand it. When you find a paper worth digging into, it might take days+ to fully understand it, depending on the depth of the paper and the field.
>How to organize what you have learnt
For organizing papers themselves, Mendeley is a nice tool. You can tag them, put notes, organize them into folders, etc. For organizing the actual knowledge, I've used a variety of tools like OneNote, Evernote, .txt files, etc. Organize it roughly by topic area, keep notes, and keep references to where you learned the thing so that, when in doubt, you can fall back on the original source.
>How to keep up with change
As above, arXiv, conferences, and journals. You could also try to follow science news in the field, or some sort of blog, but I think that sticking to the original sources might be your best bet if you have the bandwidth for it.
Let me know if you have any other questions? Also, I'm sure if there are others familiar with research here, they might disagree with what I've said, so feel free to correct me/start a discussion about best practices..