+1 to both Alexsandr's and jakebeal's answers, especially jakebeal's recommendation to look at review articles, i.e., articles that review the state of the art in a particular topic, summarizing many individual contributions and articles. Reviews are definitely something to look out for.
Depending on your specific field(s), there may be entire journals set up to publish nothing but reviews. These are the journals you want to find and set up alerts for, as per Aleksandr's answer.
Three things I'd like to add:
First, try to attend a conference once in a while if your budget permits. It's a lot easier to figure out who the central people in a field are when you see who is on a conference organizing committee, who is invited for keynote talks, and who generally makes insightful comments at others' presentations. Get their cards, google their names, find out what they do, and follow them as appropriate, by subscribing to blogs or Twitter feeds, friending them on Facebook, or following them on ResearchGate or Academia.edu.
Second, develop the art of skimming. You simply won't be able to read everything, even if you restrict yourself to review articles. With any paper, start by reading the abstract. If that does not appear to be useful, don't feel guilty about putting the entire article aside and focusing on a different article that is helpful.
However, do also develop the art of not only checking what's immediately relevant, but also what is only tangentially related to your main focus, because this is how you acquire breadth, as opposed to depth. I'll save any article that sounds even vaguely interesting and have made it a habit to at least skim one of those on a daily basis. (Yes, I do need to explicitly track this, because otherwise this daily reading will be crowded out by short-term issues, and I'll never get around to reducing my "unread" pile. YMMV.)
Edit: Regarding my first point, on conferences, @Josh comments that it might be difficult to network one's way into those.
At least in my field, you can simply attend a conference without presenting anything, so there is nothing to stop you from attending. I don't know whether there are conferences that only allow you to attend if you present something, but I would be surprised if such restrictions were common.
Conversely, large conferences will eagerly welcome new attendees. For instance, the American Statistical Association, at their Joint Statistical Meetings, have "docents", long-time attendees that are available to show first-timers how to navigate a convention center full of thousands of statisticians.
I agree that there is a bit of a chicken-and-egg problem in finding the right conferences to attend, if you want to attend to get an overview of a field... because looking for an overview by definition means you don't know enough about the field to choose a good conference. You will likely need to do some homework about this.
- Look for good publications, check which academic societies sponsor those publications, look whether they organize conferences.
- If you found someone who does good work, see what conferences he or she tweets about attending.
- In computer science specifically, where most of the science is done via conferences rather than via journals, once you find a good publication, check what conference it was published in, and more importantly, what conferences its references were published in.
The entire "find a good conference to find good researchers to get an overview of a field to find a good conference" loop will likely need a few iterations. But there is positive feedback involved: the more high quality people/journals/conferences you know, the more new high quality people/journals/conferences you will get to know, because your network will gain dynamics and traction!
In fact, I started out in my now current field as a blank slate in 2006, with a completely unrelated Ph.D. and no academic connections to this field whatsoever. So I simply googled around, found some papers, then a journal, then the journal's sponsoring association, then its conference, simply attended this conference in 2006 without knowing anyone whatsoever, chatted up everyone I met, contributed a little to the associated practitioners' publication and pretty soon felt very welcome indeed in this particular community, although I am of course not an academic per se. The approach I propose works.