This is a harder exercise than it might seem. I'll give you the same advice as I'd give someone attempting to write poetry. Read a lot of it first and absorb the unwritten shape of successful efforts you like. Explicitly, you can use the following guidelines, which I'll add to in response to suggestions:

• The article should tell a story first and foremost. For example, imagine yourself as the Ancient Mariner who has buttonholed the wedding guests and has a fascinating tale to tell.
• Have a particular publication in mind. You can if you like imitate the page layout, typographic style, use of references, etc. This can help you 'put the right clothes on' for the act.
• The article should have a distinctive beginning, and an end that refers back to the question or analogy you introduced at the beginning.

• Use analogies more than you would in a scientific paper, relating comparative magnitudes for example to comparable ones involving everyday objects. Particularly large or small numbers that arise can benefit from being explained by analogy. Don't overdo it!
• Use the occasional colloquialism if it occurs to you naturally in the context.
• Increase the human content of the article from that usually used in a scientific paper. Thus, don't say 'Einstein's relationship tells us that the distance travelled increases as the square root of the time." It is better to add some relevant background and you could say, for example, "Einstein puzzled over the mechanism of Brownian motion early in his career. He showed that the distance a particle moves away from its starting point increases as the square root of the time you watch it. This result was considered so important that it formed part of his Nobel Prize citation." The trick is to put in enough to keep up the interest but not so much as distracts from the underlying story.
• Choose a subject you feel confident with. To write a 'popular' article you need to know much more than you're going to put across, in order to set the right context. Don't write about a topic that you're struggling to understand yourself.
• Don't waffle where you can be accurate and precise. Your article should have the authority of being written by a science graduate (or imminent graduate!). You are not trying to imitate a working journalist but do a specific job rather better.
• Don't be frightened of putting good science into the article, but remember you are not trying to write an encyclopaedia article. One technique to use if you are covering a broad area is to summarise the range of the topic and then home in on a couple of specific aspects.
• Include an illustration or illustrations appropriate to the publication.
• Read over the final result and check that the style and approach is right for your target publication. If it's meant for the New Scientist, make sure it doesn't sound like a Daily Mail article, and vice-versa.