Style is one of the less important selling points for a story. The plot, the characters, the setting need to be good, but people do not buy stories because they are well-written. Still, I seldom read published work nowadays where the style isn't at least competent and workmanlike, so some style needs to be developed.
It's very difficult to give good, straightforward advice on how to develop one's style. So, I am giving some sideways advice.
First off, your style is built up of words. Therefore, getting to know words is learning your basic tool box. Vocabulary building exercises may help, but you understand a word best if you meet in its native habitat, in the wild. Read widely. Get to know many words. You can't use "amble" or "trudge" instead of "walk" unless you know "amble" and "trudge." Good words can lead to the possibility of boiling down long phrases into a single word.
Of course, it does open the possibility of overloading your prose with sesquipedalian verbiage, rendering it ornate and unintelligible -- but writing is full of risks. Practice helps avoid them.
In particular, if you are writing works that do not take place in the current day, you probably want to read old books. In English, Shakespeare might be pushing it, but Jane Austen is a good aiming point. Start with the more recent ones and work your way back. That allows you to build up your knowledge gradually. Once mastered, that knowledge enables you to see whether a particular word (or metaphor or idiom) is modern. Archaic style is a notorious trap for the fantasy, but a kind of timeless English, such that it could be read easily any time in the last few centuries, works better for conveying that the readers are no longer in the fields they know. It is perhaps impossible to rid your style of all terms that are laden with the current day -- how many people still realize that "strong suit" comes from bridge, and therefore is anachronistic before its invention? and that since it requires playing cards, also requires cheap paper? -- but it helps shift the scene.
Reading alone, however, may leave the words in your reading vocabulary. They will do your style no good unless you use them. Therefore, while you are writing, you have to question the words you use, considering whether "give up" or "yield" or "surrender" is the appropriate term.
In aid of that -- well -- here is your whip. Practice cracking it a bit. And here is your chair, to fend it off. Now, let's go into the cage.
snarl
crack
Now, this is the wild and untameable thesaurus. See how it crouches and glares at you? It hates you and wants you to look like an idiot. Give it the slightest chance, and it will pounce on your manuscript and pepper it with subtly wrong -- and sometimes, not so subtly wrong -- words. Never use it to replace a word with another that you are not familiar with.
As a tool to remind you of the possibilities, it can be invaluable.
The second thing is, once you have the words, you have to arrange them artfully. In grammatical -- or judiciously ungrammatical -- sentences. So it helps to know your grammar.
This is less important than with words, to be sure. You can't use "amble" without knowing it, but you can write "Jill's ambling brought her to the store within half an hour." without knowing a gerund from the passive voice.
Still, besides the obvious advantages in letting you talk about the way your sentences are structured, and letting others economically point out your errors, there are stylistic advantages to knowing the full armatures on which you can arrange your words. Gerunds, infinitives, clauses (subordinate or independent), compound sentences -- it makes it easier to look at a page and think, this sentences are awfully similar, because you can recognize that they are all simple clauses joined with a conjunction. And considering how you can rephrase them is easier when you are aware of the possibilities.
I have known writers who defended "not simultaneous" structures ("Waking at dawn, he walked to the kitchen.") on the grounds that you need to vary your sentences. Knowing your grammar helps avoid this.
It helps to run across them in their native habitat, in the wild. Reading widely helps show how all these lovely grammatical tricks can be used, though nothing substitutes for using them in your own writing. Putting something in a subordinate clause helps indicate it is less important than the action of the main sentence. Things joined in a sentence are more connected than things in separate sentences, though, oddly enough, long rolling sentences tend to flow from sentence to sentence more easily. Short sentences have punch. Short sentence fragments too. Except when too many appear. Then the prose is choppy. It is generally wisest to use moderately long sentences, and reserve the short ones for things that really need the emphasis of a short sentence -- and if necessary its own paragraph. None of these grammatical effects are more than mild. Still, every bit helps convey your meaning.
The third thing is -- reading widely helps with words. It helps somewhat with grammar. What it is needed for, really, is --
No, the warning comes first. This is a writing exercise. Only in the rarest of cases does it produce anything publishable. If you try to publish it, it's NOT MY FAULT.
But, to develop your style, it helps to write pastiches of writers you admire. Great stylists are best, but the real point is to master the art of making words jump through flaming hoops rather than sit around on the page. Trying to sound like any writer is aiming for precision in writing. It works best with writers you admire. Indeed, many people just fall into it, falling in love with writers' styles and trying to imitate them. It is not for nothing that Ursula K. LeGuin dubbed Lord Dunsany "First Terrible Fate that Awaiteth Unwary Beginners in Fantasy." It's hard to imagine how many writers have churned out how many reams of eighth rate imitations of Lord Dunsany. Then, even eighth rate Lord Dunsany imitations teach you a lot about how words fit together to produce style.
Then, once you get through fits of Lord Dunsany, J.R.R. Tolkien, Patricia McKillip, and many other writers (good or bad stylists), you have learned lots of effects you can produce by putting together words in all sorts of grammatical structures.
Lots of writers is an important point. It's one thing if people can tell that a writer is an important influence on you. It's another to write only pastiches. (That warning up there is not kidding.) And for another matter -- writers are good at various things. Imitating many different writers teaches you many different things to do with your box of tools.
The fourth thing, the thing that really pulls it all together, is the habit of eyeing every word to see if it really conveys what you want as precisely as possible: whether it gives the action, the characterization, the setting, and all with the tone that supports rather than undermines them. Some rules you hear thrown about are often not only good for improving the prose in themselves but which develop the habit. Some of which could stand to be strengthened in themselves.
In the arena of verbs, you have probably heard the rule about avoiding the passive voice. This is a little weak. What you really want to avoid is any superfluous use of auxiliary verbs. Reduce the verb to one word if you can, two if you must -- and more than two if you must, because sometimes you do need those subtleties. Most of the time you need more vigor. I read sentences, "She could see the red zeppelin floating toward them." and my little editorial imp says, "She saw."
All forms of "to be" should get an especially wary eye. The passive voice, yes. Rare is the time where "She was delighted by the dance" is really needed over "The dance delighted her," and when it is, making use of the vocabulary and the habit of using it sometimes helps. "She was given control of her inheritance at twenty-five" can be recast as "She received control of her inheritance at twenty-five." The progressive voice also, unless you can't structure the sentence so as to make the continuation of the action clear without it. But the use as a linking verb is often very weak.
Especially in the construction "There was" or "It was". Two words of pure deadweight. It's amazing how often it can be recast even if you don't get rid of the "to be". "There were three trees by the road." -- "Three trees were by the road." If, indeed, you don't go all the way to "Three trees stood by the road." If you really need it because the sentence sounds dumb otherwise, you might find a way to bury it in the middle of the sentence, so it doesn't lead off: "There were six terminals by the spaceport entrance" to "By the spaceport entrance, there were six terminals."
Akin to "there is" are the phrases "most of the", "some of the", "one of the." Nine times of ten, you can just write "most", or "some" or "a" -- and when you can't write "a" you can often write "one." You really need the "of the" only when you have not made clear before then what group the phrase is referring to. Or implied it. If the king orders a man arrested in court, we will assume there are soldiers, so "a soldier" can escort the hero away.
It's amazing, when you come to it, how much description can be coaxed into an active voice -- The red and yellow flowers nodded in a passing breeze. The pool spread beneath the blue sky. The afternoon sunlight sprawled over the waters. -- though I point out that the actions chosen are lazy and deliberate ones to describe a peaceful garden. You want to load your language, and therefore need to consider what the load is. If description is vivid, it will vividly convey something that neutral language would not. A peaceful scene should not have flowers bursting with color.
The same rule applies to metaphor and simile. Neither merely conveys a description. They set the stage. It shows the point-of-view character's thinking processes, and sets mood, and conveys something of the world. A character "as pale as a prisoner being lead to execution" does more than describe pallor. Even something so simple as a princess's white gown, it matters a great deal whether it's snow-white, lily-white, pearl-white, or bone-white, not for conveying the color, but for what it implies about the princess.
A more general rule is to include as little as possible that does not appeal to the senses. "It was fall when they returned." may become "The leaves had turned when they returned" Avoiding the dead infrastructure of language helps. But it's a knack that takes a lot of working at a word level to develop.
Another general rule is to put down events in the order they occurred. "She turned when the door slammed" is less effective than "When the door slammed, she turned." Or even "The door slammed. She turned." Putting events in chronologically order not only means the readers encounter them as they occur, it frequently means you can save subordinate clauses for other uses, and simplify your prose.
But what these rules really need to inculcate is the habit of not assuming that the language will automatically convey what you want it to convey. "Style" is what someone else calls it when they come along and see how well you conveyed the story in those words.