In Elmore Leonard's 10 Rules of Writing, he wrote "Try to leave out the parts that readers tend to skip." This is excellent advice, not only for fiction, but for journalism and other forms of nonfiction.
The Associated Press has set a length guideline of 300 to 500 words for most articles, and 700 words for the top articles from each state. When I read this, I began applying it to my own writing, slightly modified for the nature of my output. I now keep my descriptive articles to 500 words or less, while I allow 700 words for explanatory pieces or essays. In every case where the first draft of an article exceeded those limits, carefully paring it down noticably improved its quality.
The limits are somewhat arbitrary. An article should be long enough to fully convey the idea or information intended by the writer. But two things make length guidelines effective. Wordy writing is often sloppy and unclear, and shorter pieces are better suited to the average reader's ability to absorb and retain information. Limits enforce self-discipline in the service of clarity.
A wonderful resource for writers aiming for brevity is the classic guide The Elements of Style, by William Strunk Jr., and E.B. White. This short book has been required reading for generations of English composition students, but it needs to be even more widely studied by anyone who frequently puts words to paper. One of the most compelling paragraphs is from the section "Omit needless words":
Vigorous writing is concise. A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all sentences short, or avoid all detail and treat subjects only in outline, but that every word tell.
Another resource for learning brevity in composing sentences is twitter. When I discovered twitter I considered the 140 character limit evidence of the short attention of the public. As I used it, though, I found it to be an exceptional laboratory for putting ideas into short sentences. A good exercise is to form a thought which would normally require a paragraph to describe, and try to fit it into a 140 character tweet.
Brevity encourages clarity, and clarity should be the goal of all nonfiction writers, and most authors of fiction. Setting length limits, and carefully eliminating extraneous words and sentences is a skill every writer should learn.