Write lots. You said it, but it bears repeating.

Next, get good feedback on your writing. For me that's the second most important thing.

Good feedback is feedback that tells you what effect your writing had on the reader. (This means that things like "I didn't like it" are rarely useful feedback; "I was engaged until the third paragraph, when your mention of dolphins felt unconnected to what came before" is great feedback.)

Having your writing reviewed by a group can be harrowing but is also a great way to improve fast. Diversity in the group means that most of the major improvement areas in your writing will be spotted by someone.

I don't have any studies to back that up. It's hard to find evidence-based opinions on improving one's writing. Writing is an extremely diverse activity: creative writing, persuasive writing, informative writing to name but three categories off the top of my head may have very different optimization criteria.

You may be interested in a book I'm currently reading, Anne Flaherty's The Midnight Disease. It's a neurologist's take on writing; short on advice but long on fact. It does a good job of sorting through productivity, creativity, inspiration and so on in terms of "you are a brain".

I've read a bunch of other books on writing - Wiiliams Style: towards clarity and grace (I don't remember much of it), Lamott's Bird by Bird (which I found useless), Elbow's Writing with Power (very fond of this one and the freewriting exercise in particular), Goldberg's Writing down the bones (don't remember), Richard Gabriel's Writer's workshops (best advice I've ever read on writing), etc. You could do worse than Alicorn's "saturate, distill, improvise" approach.

Writing well, it seems to me, depends on getting a great many small things just right - not on improving any particular single aspect of your writing. You need to have something interesting to say, to care a lot about it, to organize your ideas logically, to make sound arguments, to lead your reader through it without losing them at every corner. You also need to engage the reader by making your ideas relevant, to be memorable through vivid imagery, to have a sense of rhythm. You need to know when to be funny and when to be serious. And so on - and all of this needs to be tailored to the expectations of the audience and the conventions of the genre you are aiming at. A scientific paper calls for different voice than does a story for children.

"Write lots; get feedback" may be the most general advice you can get without getting into specific things you want to improve about your writing.