1) Once you have a good lead (the opening sentence(s)), the rest of the article is much easier to write. A good lead is something that grabs the reader and makes them want to read on.
2) Try to replace abstract nouns with visually evocative language. Thus “Soviet nuclear testing in Kazakhstan left in its wake serious medical issues” becomes “Soviet nuclear testing in Kazakhstan left in its wake mothers nursing deformed babies and teens wasting away with leukemia.”
3) Make your points with quotes from or stories about individuals if you can.
4) When you’ve written a sentence, go back and make it shorter. Make subordinate clauses justify themselves. If it’s in the passive voice, ask yourself if it could be in the active voice. Could it be more colorful?
5) Write in shorter paragraphs.
6) Getting op-eds published is partly a numbers game. If you’re rejected, keep trying. If you get published somewhere, see if you can establish a relationship with the editor so they will publish future pieces.