Similar to the baseline advice to learn programming: write a lot. Read good writing, read bad writing and learn to tell the difference. Leaving a piece of writing for 24 hours and coming back to it with a fresh pair of eyes to edit helps. Someone else's eyes also helps, similar to how code reviews help.

Reciting your writing out loud helps too. If it isn't in the desired tone and/or it doesn't sound natural, rewrite it. You may find you need less adverbs than you think.

Books on writing style and techniques help in the way books about algorithms, paradigms, design patterns and other facets of programming help. The key is to implement the ideas you learn in your writing.