I feel I should have a good answer to this question, since I've been writing about mathematics for the general public for many years -- but after some thought, I'm not coming up with any specific advice.
But I can say this. To write about popular mathematics well, you must write well. Your explication of the main idea can be as clear and correct as you like, but if the sentences lie dead on the page, no one is going to read your column. And this applies doubly, given that you're asking people to read about a topic that, in most cases, they don't think they care about.
So I think the best advice you're going to get won't come from us, but from people and books that have something to say about English prose generally: Strunk & White and its successors.
The short version of all such books: Vary sentence structure. Read what you write aloud. Imitate things you like. Avoid cliche. And, above all, cut all words that are not doing work.