I've improved most dramatically at writing by getting very specific feedback from people who are clearly better than me. I consider myself lucky to have had a small handful of teachers and professors willing to put in the time to critique my writing on the sentence- and word-level.
Recently I had a work of fiction of mine minutely critiqued by a professional author and experienced a similar sense of "leveling up". For example, I've thought for years that I understood what "show don't tell" means. But my gracious editor in this case was able to point out multiple instances in my story where I was "telling" when I could be "showing". Once he pointed these out, I understood on a deeper level what to pay attention to.
One interesting thing about getting feedback on writing is that someone who is truly better than you can usually provide suggestions that you immediately recognize as correct. You may think your writing is fine, even great, but you'll recognize true improvements as being obviously correct and better, once pointed out. The process of becoming better at writing is the accumulation of such individual corrections.
I think the overarching thing to do is to simply write more. To that end, there are a lot of ways to make this happen. For example: participating in NaNoWriMo, committing to writing a sequence of articles about topic X, engaging in discourse online, summarizing research papers for a larger audience, writing guest articles for a blog, or journaling.
As for improving your actual workflow, I think that the Typical Writing Class you take in school largely gets it right. For example, writing outlines / summaries before starting the actual writing, asking people to proofread, have several drafts / edit, and try to imagine reading it from the reader's perspective w/o the extra context you have as a writer.
(I think most of the dissatisfaction I had with the skills taught to me during class had a lot more to do with the context of "Oh man, I have to write this thing using this technique for school and not of my own volition?" rather than the skills themselves not being very good.)
The short answer is: practice practice practice.
The longer answer that you need to find a peer group or community that encourages practicing and gives meaningful feedback, because writing something you know no one will ever read is a stressful and exhausting chore.
To lay our my priors and sources, I've been an amateur writer for about ten years. I started with fanfiction back in college, and I've since been published in a few sci-fi periodicals. I'm told I'm pretty good, though I certainly didn't start that way.
A lot of professional writers will say that fanfiction is bad practice for becoming a writer -- that it teaches bad habits, that it disincentivizes world-building, and that it distorts expectations by giving the writer a very friendly audience. All of those criticisms are fair. But because fanfiction gave me a community I enjoyed writing for, over the last ten years I've written about 900,000 words.
That's eighteen standard-length novels. Imagine writing 18 novels you knew nobody was ever going to read, simply because you "needed practice." I doubt I could finish one.
There are lots of nuanced steps to becoming a good writer: learning to construct scenes, leaning to show instead of telling, learning to establish character voice, learning to edit, etc. But you can't execute any of them if you aren't practicing, and to practice you need people who will read your writing and encourage you to continue.
I'm not really interested in writing quality fiction but in the kind of writing that expresses ideas effectively and makes the audience want to engage with them.
I have personally written 10000 comments on LessWrong. I don't have statistics about my average amount of words/comment but it wouldn't surprise me if I wrote 900,000 words on here.
While I don't think my writing skills are completely horrible, I don't think I'm in the top 10% within this community. It seems that writing the words alone isn't enough.
To create influential writing it's not only necessary to have good ideas but also to be good at writing them up. What's the best way to improve writing skills?