Unfortunately, my more extensive experience in reading the newspaper is that most journalists don't follow this advice, especially now that the Internet provides limitless space for their articles. Many times, article-reading can turn out to be very similar to searching for a word in the encyclopedia or dictionary. Trying to understand one thing ends up trying to understand a chain of different things.
For learners of other languages, this can be an extremely frustrating experience. Luckily, there are several sites that shape the articles for ELLs, such as The Bangkok Post: Easy English News and the Simple English Wikipedia. Both simplify existing articles that can be compared to the original if you want, and the Bangkok post also has listening components.
The Bangkok post is designed for locals in Thailand. It has glosses of difficult words in English and Thai. The news is also more relevant to that region, but it can easily be expanded into a culture lesson or related to news relevant to your own students. For example, the article on smuggling could be related to the problems America had with Britain just before the Revolutionary War or to the more recent standoffs America has had with pirates.
Or for my own EFL setting, I could have students discuss their experiences with knock offs brought in from China, shoddy bootleg DVDs, or the Russian Mafia. I find it very difficult to watch V for Vendetta in Russian with the same guy dubbing all the male and female roles!
The Simple English Wikipedia, on the other hand, is designed to be readable by children and adults learning English. I figured the best way to test its usability would be to look up psychology:
Psychology is the study of human behavior, thought, and feeling. It deals with all actions and reactions of people. Because behavior is difficult to study as a whole, psychologists often only look at small parts of it at a time. Psychology overlaps with many other fields including Medicine, Biology, Computer Science and Linguistics.
Not bad! Even without reading the whole article, I think students will find these explanations more helpful than short dictionary entries. And if this version is even half as addictive as the full version of Wikipedia, your students will be reading junkies in a week! I also love that encyclopedias give students the opportunity to discover things in the target language that they didn't even know about in their L1. Just yesterday it helped a Portuguese student discover the walrus. After reading about it in English, he could click the Portuguese button on the left and read a similar entry in his native language-- after which he was certain he'd never heard of this majestic creature!