Perhaps you should be asking how NOT to write popular mathematics well. The moment you create a template based on these excellent answers, you would lose your authentic tone or signature if you will.
So it depends on what popular mathematics you would like to read. For a student like me I always enjoy author who can maintain certain lucidity with his natural tone and who does not insult the reader's intelligence. By latter I mean who is adept at simplifying without dumbing down for audience. (For instance, I believe when Jeopardy! initially aired they wanted to "dumb down" the show but Merv Griffin did not want so.)
Recently I read Stalking Riemann Hypothesis by Dan Rockmore and because of the nature of the content author intentionally paused to explain concepts such as random matrices, Tracy-Widom distribution, eigenvalue etc. which would be accessible to even high schools students yet capture attention of mature readers. Rockmore used brief biographical snippets of people involved which made his book as enjoyable as Keith Devlin's The Millennium Problems and Mathematical Mountaintops by J.L.Casti.
To recapitulate 1) find a style that works for you; and 2) choose an interesting topic and your audience.
To permit me a transcendentalist quote:
"Do not go where the path may lead; go instead where there is no path and leave a trail."
