I've recently come upon this subreddit and to be honest it's a bit confronting. I always knew my relatively good history knowledge was a case of big fish in a small pond but after looking at all the questions and thinking "I could answer this but in nowhere near the depth it deserves" I am curious as to how the great people of this sub moved from this kind of general shallowness to knowing their specific fields so deeply.
Was it a movement whilst at university, during post grad or earlier; did you specialise in the history of your heritage or in something that was interesting or easy for you to gain primary sources on?
The obvious answer is "I read a LOT," but that's also not very helpful.
More to the point: I read a lot of Very Important Books in medieval and early modern history, in focused categories: Reformation history, medieval Mediterranean, late medieval literature, sweeping narratives of The Middle Ages, etc. The single best resource for doing something like this, IF your topic is one that is studied academically (not all are!), is PhD exam reading lists. Boston College's history department has a bunch of theirs online, but you can find others if you Google around. (And if anyone is interested in a medieval subtopic, PM me even if your interests don't line up with mine. I have resources.)
A method like this, though, is fairly dependent on access to an academic library or a willingness to obtain what books you can through...various means...since academic books are often cost-prohibitive to buy and/or out of print.
after looking at all the questions and thinking "I could answer this but in nowhere near the depth it deserves"
Also, please keep in mind that most of us are looking at our books/articles/notes for most questions. I can think of a few I've answered off the top of my head, but only because I'd answered related questions before so the evidence was fairly fresh in my mind.
Reading is to get a sense of the broader context, and where to look to find the answer to a given question.
And finally: almost all of us are deeply, DEEPLY ashamed of our first few or many posts in AskHistorians. Writing an AH answer is a particular writing skill like any other. Some people might be ridiculous naturals from the get-go, but it takes most of us some time and practice to get into the flow of things. Shockingly, readers never seem to notice or care in the slightest. :D
I think one of the key things isn't knowing things by heart, it's knowing that hey, source X will have what I'm looking for, and that source Y will have something slightly different but complementary.
Knowing that kind of thing comes after a lot of practice researching and becoming familiar with sources in your area. To be honest (and somewhat self-serving), answering questions here is a low-pressure way to do that kind of practice.
As someone who didn't start out in this discipline, I want to echo /u/sunagainstgold's "I read a LOT" answer. I was a writer and English professor who taught research writing. I started apply the techniques I was teaching to my students in topics I wanted to understand myself and suddenly realized I knew a lot about things most people don't know much/anything about. I don't consider myself an expert yet, but with practice from AH and getting into a second master's program in International Studies, I'm hoping I'll get there. :)
The key really is to focus on the area you're interested in and keep reading quality, well-vetted sources on it. Knowing what is a quality source is extremely important: does the source have an educational background in this area, is it corroborated with other sources or does it conflict, is there an attempt at an unbiased opinion with facts, statistics and examples to back it up, etc. Keeping notes helps tons. Knowing when to quote your outside sources is an art in itself. Basically, if it's something that supports your point and the original language is important to the context or you can't say it better yourself, quoting directly is a good idea. And always, always cite your sources when you're done.
This is just a few tricks off the top of my head, but the only thing that will really improve anyone in any area is practice. So I recommend try not to be daunted; we're all learners here.