Writer, write, write, and write some more. If you are having a hard time writing, then write it in your native language and then rewrite it in English (but don’t translate it). Remember, it’s about the ideas not conforming to the meaning of your first language. Something I have always told students is that they need to write often and read journal papers in the journals they want to publish in. The truth is that no one will ever become a better writer by reading about writing in theory. The more you write and the more you read, the better writer you will be. It’s that simple and anyone who tells you that you can become a better writer without you writing more and often is lying to you.
For academics who want to improve their English, the single best way is to read scientific papers, news articles, blog posts—everything you can find—in English. Certainly the source of unclear English is not usually any lack of understanding—our customers are highly educated. You can pick up a lot passively from reading published texts: a pre-conscious understanding of what sounds natural, what phrases are most often used. With these templates lodged in your memory, it becomes easier to express English in terms of English you already know (consciously and unconsciously) is right, rather than trying to translate in your head from your native language.
In addition to my advice for authors wishing to publish many papers, I would say the best approach is to have a reputable editing company edit your papers and then pay close attention to the kinds of changes the editors make, and with each new paper, try to use a few more of the type of constructions the editors use. Also, authors could try out Uni-edit’s TARGET tutor service for a few jobs, which provides explanations for edits and advice about how to use words and phrases.
I agree with Daniel: Practice and practice. Always write in English as a draft and, if possible, ask at least one native-speaker to proofread and give comments so you can learn from the accumulative experiences.
I think it is good for a non-native speaker of English to read as many international journals related to his/her research area as possible. I think it will improve his/her academic writing skills. Studying English and talking with native English speakers can help you improve English, but it’s not enough for academic English.
Like Mark said, reading, of course, but writing more in English will help you improve a lot. Authors will further improve if they read the editor’s work.