How can programmers improve writing skills?
I’ve commissioned a lot of programmers to write books, so I feel I can answer this one. Except that I only ever commissioned programmers who were already blogging. By reading their blog I could get a cast iron guarantee of their ability to write well.
There is an outside chance that, rather than the best writers choosing to start a blog, that the ones who began blogs were the ones who became the best writers.
So begin a blog. Explain something to someone. Choose something you know something about. Explain it to the people who are just below you in knowledge level. That bit is key. You will need to learn not to speak to peers using jargon and shorthand, but in full prose using easily understood phrases, analogies, summaries. You will need to learn to keep it short to keep them interested. Mostly that’s it.