While I am perhaps not the best person to talk about this as I've only had one submission accepted, my recent time spent with the Firehose has demonstrated to me that most people have a hard time crafting an acceptable story submission, in spite of the numerous examples on the front page. The following is just a list of hints and tips that might help someone assemble a story submission that makes sense.
Slashdot, being a news aggregator, is about links. A submission without a link is like a hot dog with no dog. But beyond simply having a link, there is the matter of context. It is never appropriate to have a link whose text consists of "click here", as in Click here to visit Slashdot.org. Nor is it reasonable to link the URL, as in "you can visit Slashdot at http://slashdot.org". If we want to know the URL, we can mouse over the link: "You can read more at Slashdot". Besides general good etiquette, Slashdot gathers all of the links from the submitted story and places them in a sidebar block titled "Related Links". This block makes much more sense when you make descriptive links. The only kind of submission that might not need a link is an Ask Slashdot.
Use the <blockquote> tag sparingly. The entire story submission will be blockquoted anyway.
Watch your spelling and grammar. Few things are more disorienting than a missing word, or one spelled so incorrectly that it could be a different word entirely. Something like half of the story submissions to Slashdot have one or both of these problems.
Pay attention to the length of the subject field. You are only permitted a fixed number of characters for the subject of story submissions (or anything else with a subject line here on Slashdot.) If you're not paying attention, you can easily end up losing characters off of the end of your title.
Make sure you submit into the proper category. "Enlightenment", for example, is not meant in the Zen sense. We're talking about the window manager here, and the icon reflects this fact (although there's not been much news about it lately, so one can't be blamed if they've never seen the icon before.) Think carefully and read the names of all the categories if you're having a hard time deciding.
Don't just copy and paste someone's press release (or part of one) into the submission field. Explain why it's worthy of being called news!
Finally, don't use a story submission as your personal crusade. Slashdot is about discussion. If you want to engage in lengthy discussion, then wait for the story to be approved, and go post a comment. The longer your submission gets, the less likely it is to be approved.