Reread your story, looking for connections between characters, events and settings that you may not have been consciously aware of while you were writing. Think about whether you can deepen any connections or meanings that you have discovered.
Look at your story's ending. Ideally, an ending should seem both unexpected and inevitable, and all the threads of the story should come together. Think about whether there is anything you can do to enhance the ending.
Reread the story to see whether your main character has changed in any way. In a literary short story, the change can be extremely subtle, almost imperceptible, but it does need to be there.
Reread the story to see if there is anything that you need to cut out. In a literary short story, everything, even details of the setting, needs to be a part of the story's meaning. Anything that doesn't contribute will have to be cut.
Reread the story to see if your characters' words, thoughts and actions ring true. If anything seems unbelievable or sentimental, then revise.
Reread with an eye on word choice. Can you replace vague words with words that are more precise? Is the tone consistent and does it support the mood of the scene?
Put the story away for at least several days. Then when you come back to it, you will see it with fresh eyes. Reread it again, and see if there is anything more you want to add, delete, or change.