Here is one frequently successful format, reproduced in full. She will then encounter the first page of your story, and, assuming that it is merely a continuation of the letter, will read further. As getting the editor to read the story is one of the would-be author's major challenges, there is much to recommend this technique. Another, similar, technique, is to retell the story in such detail that the book or story itself becomes superfluous. Many such cover letters are themselves published to wide acclaim.
Many authors find it prudent to threaten or cajole the editor in some way.
Editors who fear for their careers, editors blinded by greed and lusting for power, are more willing to take chances. Unlike most other fields of endeavor, the task of writing fiction is one in which a certain degree of mental impairment is a positive boon. Editors know this. You should take advantage of it. Spice up your letters with mention of the shafts of light coming from your eyes, or discuss the merits of one brand of aluminum foil over another in shielding your skull from alien thought beams.