Over at Rawle Nyazi's blog he had a good post on why Game Masters should be, and need to be, well-read. That post followed on from a post at the Castalia House blog on how short fiction can completely eliminate the need for supplementary materials in a tabletop RPG.
This harmonizes with my insistence that all you'll want from the publisher is a ruleset, and quite frankly you don't need to buy that either anymore- you have since the year 2000 (and you can find other free option, similar to and divergent from the d20 System baseline). That assumes that you want to bother with someone's else design at all, and I don't as often as not anymore.
So, what should you--as a fan, as a gamer, whatever--do to Git Gud at this thing you love? Well, I've been harping on it over this week: READ! Read the sources the creators draw from. Read the philosophers they rest their assumptions upon. Read the histories, biographies, mythologies that they're taking from. Read widely, read deeply, read for comprehension- not speed. Oh, and a note: there are different modes of reading for different purposes, so learn and master them.
Think this isn't relevant to Your Thing? Remember what I said yesterday about Thrawn being Sun Tuz? That's proof of relevance; once you've read The Art of War a few times and know about the Warring States period in China's history you can see where Thrawn's coming from in his approach because you read that in Sun Tzu. (You can add Clauswitz and Machiavelli to that category of reading.)
Remember my complaints about the Monomyth being all over Hollywood? Well, Joseph Campbell didn't operate in a vacuum; reading, at the least, The Hero With a Thousand Faces will get you into a place in your brainmeats that will (a) ruin your ability to read/watch crap and (b) appreciate the brilliant stuff even more when you encounter it.
Love your mecha? Go read Starship Troopers. Like that? Go read the Lensman books; that's where Powered Armor (and mecha) come from. Ditto your Jedi, Green Lantern Corps, and similar Supercop organizations in popular fiction. Adore the fleet battles of Legend of the Galactic Heroes? Go read the accounts of ancient warfare through to the Napoleonic era, which is where a lot of the memetic references come from- not so much with actual naval history (though that's worth reading in its own right). Fascinated with the Autocracy-v-Democracy theme? Oh man, there's a whole world of philosophy and theology to follow there; that's worth a post to itself, and there are entire blogs devoted to it.
Do you see where I'm coming from yet? Do you see how, and why, reading/watching/playing more than Your Favorite SF/F Brand can only make your enjoyment of it better? Well, how about making you better able to participate in the world at-large, and at higher levels of complexity and sophistication, than otherwise is the case- things that can make your working life better, in many cases.
Read, dammit! So much of what I'm talking about is in the library, or published for free as public domain books, that you can do this for nothing more than the cost of the time required to get a library card or have an e-reader handy. It's nothing but good for you, and the more you do it the more fun it becomes.