I'm going to tackle this question a little less from the perspective of the writer, and more from that of the reader. That will help to keep us really clear about one thing: there are a LOT of different good prose styles out there. And each of us will hate at least some of them. Yes, you heard me: people can hate really good prose. That dense novel that you find way too full of words? It can still be really well written (and someone else is drooling over it). And while Hemmingway took spare, undecorated writing to an extreme that just cries out for parody, much of it is nonetheless a model of good writing that wastes no words, and as much as you hated reading The Old Man and the Sea in 8th grade, many people love it. To complicate matters, styles and fashions change, so that the prose that was seen as artistic, or even easy to read/popular fiction (think Dickens) at one time may seem affected or difficult in another era.
That does NOT mean that all prose is good and it's just a matter of taste. Some things we can pretty well agree on: good prose at least follows the rules of grammar, spelling, and punctuation, or violates them consciously and for a good reason. It is coherent (some texts from the Modernist period, in my opinion, push the limits on this. They got declared "literature" and far be it from me to argue, but really there are some I won't name who I think are laughing at us all being so serious and trying to understand them). Good prose, in my opinion, is transparent. You don't notice it, you don't think about it at all when you are reading. It doesn't stand in the way of the story. If the prose is really good, you occasionally come up for air and think, "Gadzooks, that couldn't have been better said if a thousand Pulitzer-prize winners thought about it for a thousand days."
If the prose is to not get in the way of the story, not only must grammar and spelling and punctuation be correct (those things are only noticed when they are wrong, not when right), but it must flow. You must be able to read it aloud without tripping and stumbling and wondering at the end of the sentence where the beginning went. It doesn't use the same word five times in a paragraph; it doesn't use twelve words to do the work of three; it doesn't use a string of semi-colons to run together multiple sentences (yes, I did that on purpose).
And how do you write good prose? For most of us, we start by writing truly awful prose, and then (wait for it!) we revise. We hunt for words that are overused. We double-check homonyms. We do searches for our own pet words that we love to use, and then we axe them ruthlessly at nearly every appearance. We do a search for the letter combination "ly" and ask ourselves at each adjective if it strengthens or weakens the writing. We double-check the meanings of words (and if we have to look it up, we ask ourselves if maybe, just maybe, a simpler word would serve better). And we read it aloud. Yes, the whole thing. Maybe more than once. If we can, we get others to read and help us find our weaknesses, or locate the sentences that stumble haltingly across the page rather than flowing musically from our tongues.
Oh, yes. And we read extensively, and make sure that what we are reading is well-written. Our brains absorb the examples we present them.
And then--and how you do this is up to you, but it must be done--we get an editor. Ideally, we get two--one to read early on and tell us if the story is working, and where it doesn't. That's a different issue. But now the story is great, and we are polishing the prose. And ultimately, we can't do it alone. I hear a thousand Indie authors out there protesting that they can't afford an editor. Fine. Find an alternative. Yes, a pro is probably better than your old friend who became a high school English teacher. But that friend, especially if he'll do it for an acknowledgement in the front of your book, or a couple hours helping him move, is better than no editor.
Because no matter how good we are at the language, awkward sentences we have read thirty times will escape us. We will never see all our own errors. No one else will see all of them, either. But as we used to say in grade school when teased about wearing glasses, four eyes are better than two. Or two brains better than one. When your editor returns your MS, think about each recommended change. Why didn't she like that word/sentence? What's wrong with this punctuation? And oh, yeah, I guess I did mean "its" rather than "it's". Make the corrections and hope that some of what you learned sticks in your brain for the next time.
Repeat the process until you die of old age. Maybe, if you are lucky and have enough stamina, before you are done you will have written some truly good prose. If you are doubly lucky, it will have a great story to tell.
Then you will have done what you set out to do.