I want to make an admission first, which is that Orwell has been my favorite writer, the one who's had the most sustained influence on my development as a writer, for the last three decades. I've read his essays over and over, and have always found them to be exemplars of great substance combined with unrivaled style.
Orwell didn't become well known as a writer, nor financially successful, until the final five years of his short life. It wasn't until his novels Animal Farm (1945) and Nineteen Eighty-Four (1949) were published that he became known in the United States. He died from tuberculosis in 1950 at age 46. He was mostly an unknown journalist specializing in book reviews and essays.
Writing was hard for Orwell, especially as his health deteriorated later in life. "Writing a book is a horrible, exhausting struggle, like a long bout of some painful illness," he wrote in "Why I Write." So why did Orwell write? Partly for the aesthetic pleasure of putting words on paper, the pure satisfaction of having a piece of writing flow and reach a satisfactory destination. But mostly because he was seeking to right a wrong, to expose injustice. Much of his writing is against the repressions of totalitarianism, imperialism, and (yes) the excesses of capitalism, and in favor of working-class people. "My starting point is always a feeling of partisanship, a sense of injustice," he explained in "Why I Write."
Orwell's essays are clear and meditative and wonderfully structured. Orwell is always breathtaking in how humble he is in his erudition. He treats the reader as an equal partner and his essays feel like a guided tour given by a curious, learned friend.
So what does Orwell teach us about writing? First, that clear thinking is the key first step to clear writing, and that bad writing makes clear thinking impossible. Orwell believed that there was more bad writing than good: "vagueness and sheer incompetence is the most marked characteristic of modern English prose," he bemoaned in his classic 1946 essay "Politics and the English Language."
Orwell offers a number of recommendation to think and write clearly. For example, writers should always prefer the active voice over the passive. Using the passive voice and telling the reader that "mistakes were made" (sounding like some evasive politician under indictment), only makes writers seem complicit in the lack of responsibility the sentence reeks of. To use the active voice and write "I made a mistake" or "[Insert politician's name here] made a mistake" allows us (and the politician) to take responsibility for actions and begin to do something about it.
Good writing, like right conduct, must be unafraid to take responsibility. Somebody is writing the words, so writers need to be brave enough to show the reader who they are and what they believe. Even being passive and evasive let's the reader know who you are.
Orwell was nothing if not precise with language. Clear thinking is related to seeing things clearly, which means describing what you see with exactness. For this reason, Orwell attacked cliches and vague language. He asks writers never to use cliches and metaphors they've seen elsewhere in print. Make things new, he asks, even if that requires the hard work of looking with fresh eyes and writing with fresh language.
Orwell demands that writers think concretely, not in vague abstractions that lead to cloudy writing. As he explained in "Politics and the English Language": "What is above all needed is to let the meaning choose the word, and not the other way about . . .When you think of a concrete object, you think wordlessly" and then look for precise words to describe the object. Again, thinking and seeing clearly must be a prerequisite to good writing.
The first goal of good writing, according to Orwell, is to be understood. To do this, he suggests in "Politics and the English Language" that writers eliminate needless words (cut out the fat), prefer shorter words to longer ones (in other words, don't write to impress your reader), and avoid jargon as much as possible, preferring to translate said jargon into layman's language.
There's a lot more that Orwell teaches, but you can read him for yourself. I'd suggest you start with the two great Orwell essays cited at length herein: "Why I Write" and "Politics and the English Language." If you like those, then start reading any collection of his great essays. You'll find yourself in the company of a great writer and teacher, one who'll provide you with a lot of great lessons on writing and thinking clearly.