An engaging story has only a few vital needs; the rest remains within the artistic domain of the author.
The most obvious necessity, and the one from which I'll build the other suggestions, is a definite plot. Ideally, that plot should be well-paced and smooth. A hint for finding the right tempo of a scene: Pacing of the plot tends to correlate to the emotions felt by the characters, and so those emotions need to have a definite form.
The subtleties of a character's feelings can dictate whether the story, say, tumbles frantically forward or crawls forward in dread, and so the author needs to understand how to create believable emotion. How to do that? Believe it or not, physical sensations are often the first way that the readers connect emotionally to the characters, and this means that in terms of making a story relatable, describing emotions is far less important than describing sensations. The latter can accomplish the purpose of the former; I needn’t explain that I felt sad enough for my heart to crack if I’ve already described the taste of my tears. Thus, good sensational descriptions should pull the reader into the mood of the narrative without absolutely necessitating too many other devices.
As far as those descriptions are concerned, verb and noun choice is as important as adverb and adjective choice. It follows that too many adverbs and adjectives often over-clutter an otherwise elegant piece. For example, one could use ‘blundered’ instead of ‘clumsily ran,’ or ‘settee’ instead of ‘fancy, rich-looking couch,’ and that would result in a work that is tighter, punchier. Think of adjectives and adverbs like cushions; sometimes, it’s alright that the descriptions feel soft and loosely-knit, but at other times, it’s best for the readers to be hit in the face with the power of the words.
Of course, this must vary based upon the voice that the author wishes to achieve. A younger voice might indeed say ‘fancy, rich-looking couch,’ whereas an older or more sophisticated voice could use ‘settee.’ And, on this track, voice is truly vital to a story. Many a novel has been panned because all of the characters’ voices are interchangeable. If writing is a form of art intended to capture a form of reality, then it must mirror the truth: No two people have the same mannerisms, habits, speech impediments, tics, pet peeves, favorite words, or expressions. The voice of the character is the essence of his, her, or their personality.
The story itself is actually less important than the manner in which the author tells it, but a truly engaging story is still often one whose subject is new, unconventional, or seen from a new perspective. While full-blown plot twists might be out-of-place in a particularly short story (though this is certainly conditional!), surprising elements keep a reader going. These elements can be as ordinary as a wrong name on a Starbucks cup so long as the author’s delivery remains emotionally involved.
In fact, as a rule of thumb, emotional involvement is the name of the game. Reading for pleasure is an experience of setting oneself adrift in the mind of another person, and so much of the mind is made of feeling that the landscape is quite barren without it. Even writing the absence of emotion in a character must happen deliberately; with all of the different shades--the character might be numb, or suppressing feelings, or overly analytical, or too evil to care--the writing of emotionlessness must still draw emotion from the reader. Feeling is key.
When all this has been done, the author must make sure that the damn commas are in the right spots.