After a day or two of thinking it over, I realize that saying "the process and mechanics of writing don't matter" isn't a very helpful or illuminating statement. Yes, the how, when and where of writing is not very important. Fascinating, maybe, especially with eccentric writers (but who's ever heard of one of them?), yet ultimately inconsequential. But there is more.
The what and why of writing is a different story. That's where all the action is. What you write and why you write it has an enormous influence on your writing--on your abilities, style, productivity, and success or failure as a writer.
If you're interested in what you're writing about, if you feel passionately about it, then you will write well. I'm not saying you can't write well about boring subjects, only that you'll almost certainly write well about subjects you care about, are involved in, are fascinated by, know a lot about, etc.
Tied up very closely with what you write is why you write it. If you're writing because of some compelling reason--to communicate, to warn, to connect, to amuse yourself, to persuade--your writing will reflect this. If your subject feels so important to you that you just have to write it out and make sense of it, the result will be good writing. On the other hand, if you approach all your writing like you were making up a grocery list, well, that's how it's going to read.
Passion for your subject and for the telling of it is what makes good writing. And that's good news, because getting passionate about something is an ability all of us have. It costs nothing, requires no special equipment, and asks little of you other than your time.
I strongly believe that everyone has something to say. I also believe that everyone has the ability to say it, and say it well, in writing. Now, you may be thinking, "But some of us don't even know where to begin, or if we begin, we get lost or don't make much sense." My reply is that has nothing to do with writing. That's a problem with passion or logic--either you aren't passionate enough, or you've simply never been taught to reason really well and could use a good class on critical thinking (I took one in college and it was great).
But what, you ask, about those of us who struggle with spelling and grammar and getting the right words? Again, my reply is that doesn't have anything to do with writing. That's editing, or revising, and it doesn't happen until after you write. You just need a good grammar book, a dictionary and maybe a text on self-editing.
So here's my prescription for writing well: Throw out all the writing self-help books that tell you how to do it; listen to and try out other writers' tools and methods while remaining flexible about your own; and get passionate. Get so passionate about something that you just have to share it. Go on. Feel compelled to be heard. Be driven to make sense of a piece of life or the world. And for god's sake, enjoy it. It's your passion.