If you're smart but incoherent, your ideas won't land. Only well explained ideas do. So, knowing how to get your point across matters. My approach can be summed up as this: clearly say what you mean, say it for yourself, and say it multiple times. If you do that, you write/speak well. If you don't, you write/speak poorly. There's no other requisites to be good, just tricks. The rest is about some of those tricks. But honestly, I'll say it again: to be cogent, say what you mean, a few times, and in your own words.
Trick #1: Building
If you have a complex idea, you might be making it complex or you might not yet fully understand the idea so it seems complex. Bad bankers do the first and college kids can be guilty of the second. Really, complex ideas are just combos of simpler ones. So start simple and build up from here.
(1) Usually a complex idea evolved from something else. Find what it directly evolved from (even go a few steps back if you have to) and work from there.
ex: Options are a natural example for me. Equity options come from stock (they're derivatives i.e. derived from) so whenever I'm explaining options to a newcomer, I re-explain stock first. Then, once they get stock, I explain futures/forwards, and specifically the use cases for the first derivative products, which were grain markets in like 1850 (or sometimes I bring up Thales and Olive Presses). After futures/forwards are understood, then it's finally worth it to explain options, which are a blend of futures and stock (optionality added, of course). Most people can handle shares of a company. Most people get why a farmer might want to hedge grain prices. Marrying the two concepts is where options comes in, but you need the two sides firsts. They build up to the subject at hand.
"Old before new to let an idea properly come through."
At the essay level, don't say the hot stuff without explaining its parts first.
At the sentence level, start with the old idea (which you just talked about last sentence) and end with the new idea. It helps with the flow.
(2) If an idea doesn't have much history, you can explain it by relating its simple parts to relatable subjects.
ex: One of your friends is annoyed at another one of your friends. Your social life might not have a century long history yet you may have to explain it to your special someone or your mom anyway, neither of whom will have much context on your friend group. So, before explaining the big idea of "these two are fighting", lay the stage. The easy thing is to use universally understood concepts like "My best friend is X", "My college buddies are A, B, C", "My arch nemesis is Scott Tenorman" etc. and then world build from there.
If you use things people get as building blocks to things people don't get yet, you'll have a much better time than starting in the middle of things. Help people step back and see the whole machine and then the specific pieces will make sense.
(3) If you're really stuck, try repetition to build blocks on top of themselves.
ex: I've said it before, but writing well means clearly saying what you mean, saying it in your own voice, and saying it many times.
Be careful with this sub-trick; repetition can chafe against the last point. If each repetition helps someone understand you more than the last time you said it, then it's good repetition. If not, it's bad and you should stop. You'll feel the difference between "I get it" said in agreement versus irritation.
I'm talking about pseudo repetition, where you rephrase a main point slightly. Verbatim repetition is almost always a bad idea in writing. It's okay in speeches.
Trick #2: Care
Write like you want to be read. Take care of your words and let them take care of your ideas. There's a few reasons to take this to heart.
Sub-point one: Poor communication corrodes ethos.
Like it or not, articulate people seem smarter. If you care enough to edit and cut and parse and be unique and logically structure, your efforts will create ethos. When you create good writing, it also creates you.
Sub-point two: Good heart helps.
Indifference isn't cool. Complaining isn't helpful. Preaching isn't interesting. What people remember is less what was conveyed and more the main point coupled with how they felt. If you're communicating some idea without verve, people will remember you didn't care. Write and talk with passion and people just might share your enthusiasm.
Sub-point three: Deliberate speech is good speech.
Passive voice, spoken or written, is ambiguous. If you don't have meaning behind your words, they're not only wasted breath, they're a waste of time. So, in the same way you should only say things you care about, whatever you say should be intentional. Speaking without thinking is like operating a train without laying track.
The core trick here isn't linguistic, it's mental. If you care about what you say, you'll say it better.
Trick #3: Big enough, Small enough
The length of what you're writing determines the scope of what you should say. A book can hold a complete world and support it. Great books do. An essay can contain a few big ideas about the world and support them. Great essays do. A paragraph can have a few sub-points about one big idea. Great paragraphs do. A sentence can't convey the meaning of life. Bad ones try.
Basically, if you're going to write something, you need to have enough runway to land the subject. If you decide to write about the universe, you're going to need a lot of tarmac. Don't overreach.
The structure, too, should be big enough to cover the subject, and small enough to not over-engineer it. For anything over two pages, there are some rules of thumb. You should have an introduction to pose either (1) a shared context which holds true an untruth [such as: our society states women are lesser than men] , (2) a condition or situation which leads to an intolerable consequence [such as: war leads to unneeded deaths] or (3) some relevant truth which has not been fully understood at large [such as: oil in the middle east is overvalued. Investors love these ones.]. There are other useful introductions, but these suffice as workhorses. You should then expound, in the amount of time/space you have, on the details which prove your point i.e. some truth is untrue because X; some situation is intolerable because Y; some truth is true because A yet unrealized because B. Lastly, you should conclude with either a conceptual point or a practical solution. The conceptual will lead to understanding, discomfort, and shared ideas. The practical will lead to a call to action, clear steps, and a motivated reader. In both cases, the audience should feel compelled somehow.
Notice, importantly, nowhere is a typical introduction mentioned. Nowhere in your writing and speech should a literal "tell them what you're going to tell them" approach be taken. If you want to say something, say it. Don't say you're about to say some shocking thing and steal the thunder from yourself. That's silly. And yeah, some people argue clear writing necessarily lays out the structure of the argument. Maybe -- more directly, clear writing lays out ideas. Insightful ideas reveal falsities hidden in plain sight, point out the intolerability of otherwise complacent situations, or see silent, unappreciated truths and prove them out. Insightful ideas do not come from any particular structure; good ideas stand for themselves. What is immense, however, is the power an insightful idea has when good rhetoric is laid atop it. An insight mixed with well-crafted language hits heavy.
Trick #4: Concision
This is a grab bag. Take what you like.
"That" is almost never needed. It clutters otherwise solid sentences. That sucks.
ex: "Don't expect you'll get that much from reading this."
If a word means little or nothing, drop it. Only say meaningful words.
ex: "If you're not super sure a word matters, drop it."
Don't imply words with other words.
This one is really an attack on "very" and "really".
"His writing's very bad." is more expressive as "His writing's awful."
"Her writing's really good." is more expressive as "Her writing's fantastic."
Phrases should be words.
"The example analogy was like a piece of garbage." is better as "The example analogy sucked."
Negatives should be positives. Usually, "not" is the enemy.
"That's not a bad point." is clearer as "That's a good point."
Drop useless adjectives.
"That's absolutely correct." is more concise as "That's right."
Essentially, compact language is clean. Near, but not at, extreme concision is grace.
Trick #5: Add your tint
When you say something, say it for yourself. Make it clear: your ideas come from you. The easiest way to do this is think less and only from your principles. Don't try to sound like someone who writes with big words. Write with small words -- small words are for people conveying big ideas. Your words, simply said, are for you to convey your ideas with. So go out there and think, write, and talk for you.