I’m currently reading the book On Writing Well: The Classic Guide to Writing Nonfiction by William Zinsser. As someone who is remediating his writing after a lifetime of neglect it is an amazing book. Even if you just read the first few chapters you’ll learn much.
To start: strive for simplicity. I am a wordy writer (which is odd coming from a math guy), but I now focus on removing text as I edit. This is key for scientific writing.