I like parts of Cort Ammon's answer, but I want to give a slightly different perspective. I want to answer as if what the OP really wants is a roadmap of things to do to get his or her idea to be taken up by the academic community, that is, have the idea discussed, argued about, taught in university courses and seminars, and have other people to write and think about. I'll preface my advice by saying that I have a PhD in philosophy, several publications in good journals, and worked for several years as a philosophy professor (first as a graduate student, then as a postdoc) before leaving academia. In other words, I'm exactly the kind of audience someone with a great new idea should be trying to persuade. I'll illustrate with two cases. First, the case of a genuine amateur who made important contributions to Astronomy, H. W. M. Olbers, of Olbers' Paradox. On the other hand, I'll also explain why Ayn Rand isn't a brilliant thinker unjustly overlooked by uncomprehending ivory tower intellectuals, but rather just a regular, run-of-the-mill crank, just like the quacks who invent "perpetual motion machines", cranks who "disprove" Godel's incompleteness theorems, trisect the angle, and so on.
Ok, so let's say you've had a brilliant, earth-shattering discovery, that upends huge parts of our standing theories and everyday commonsense about the world. Let's call you idea p. Let's reverse engineer what it would take to get somebody like me to accept p as at least a serious theory, deserving study.
- The first, and most important, thing to get people to take p seriously is credibility. The more people have already signed off on an idea, and the more creditable those people themselves are, the more likely others are to take that idea seriously. That means publishing in a top academic journal, since the top journals are run by very prestigious editors, have well-established reputations for quality and for publishing "important" papers. There are only a few journals like that publishing philosophy in English, namely The Philosophical Review, Noûs, The Journal of Philosophy, Mind, Ethics, and Philosophy and Phenomenological Research. If you can publish p in the Philosophical Review, your paper will get read and discussed.
Olbers did publish his discoveries: including finding several comets and then the paradox. Ayn Rand, on the other hand, published her most "important" philosophical contributions in her Introduction to Objectivist Epistemology in her own journal. In other words, she didn't gain any creditability by having her ideas critically examined and vetted by others; so of course nobody in the academic community took her seriously. Self-publication is self-defeat, because the point of publishing is to gain external validation from others.
So what does it take to get a paper published in those top journals?
- To publish p in the Philosophical Review, you're going to have to do a couple of things, at a minimum: (i) explain exactly what p means in a perfectly clear, unambiguous way, (ii) show that p is actually original, (iii) provide a really, really compelling argument that p is true, (iv) show what implications the truth of p would have for a variety of other issues professional philosophers--and perhaps the general public--care about, (v) explicitly consider and convincingly response to the three or four most important criticisms professional philosophers are going to think of when they read the paper, (vi) write precisely and clearly, introducing all technical terms, making critical distinctions, giving analogies and examples as appropriate, structuring the paper in a coherent way, and (vii) write all up in about 8000 words.
Often, when cranks do submit their work to top journals, they are surprised to get swift rejection notes from the editor. Usually this is because they have simply not done one or more of the seven things listed above. Everything by Ayn Rand I've read fails this test on at least (ii), (iii), (v). Rand's epistemology is just a crude kind of verificationism---better versions of which had already appeared in print, defended by figures like Rudolf Carnap, Moritz Schlick, and others, and subject to important objections from Hempel and others. Rand never responds to objections--so it's no surprise that her work wouldn't pass scrutiny at a reputable journal. Olbers, on the other hand, published in the leading venues in his time--which was somewhat before the modern journal system was fully developed, but it still had the same salubrious effect on his academic reputation and won his discoveries important academic audiences.
"But doing all that looks like a ton of work! It would take me a lifetime to prove my idea is true, original, defend it, anticipate the most important criticisms and write it all up in a concise but not dumbed-down way!" Yep. And that's why the top journals have the incredible reputations they do--precisely because they are incredibly demanding and it takes a huge amount of skill, persistence, and hard-acquired knowledge to publish a paper in one of them. This is the point where most of the cranks will throw up their hands and engage the little pity party about how the bad old academics just can't recognize their brilliance/are afraid of the competition/etc. Nope, it's just plain old hard work and lots of time.
So how do you get the knowledge, skills, and abilities to publish like that?
- Take classes, read papers, perhaps a formal degree. Scientific work is a communal activity. If you want to get better at writing, you need to write a lot, and have people who are better writers than you critique your writing and help you improve. If you want to know more about the field, and the place of your ideas in it, then you need to read a lot of work already done on the subject--a graduate course on recent work on the topic would help get the lay of the land on the current debate on related topics. If you want to figure out what people are going to think about your ideas and what objections they're probably going to come up with, then you need to be talking to them, presenting talks at conferences, and so on to start figuring out the shape of the discipline at present.
In Olbers' case, he actually did those things. He did amateur astronomy at nights after his medical practice. He corresponded with other astronomers. He had taken university courses in mathematics and astronomy. Rand didn't, and that's why she's a crank. Since she didn't engage the existing literature, she wasn't aware of how sophomoric and shoddy her own work actually was. If she had actually gone through the difficult process of learning the discipline, she might have made important contributions, but she did not.