Begin with a critical reading of the story. Try to move beyond a gut reaction of "I like this story" or "I don't like this story."
Analyze your reactions.
Maybe you noticed a particular theme, like death or male/female relationships or the American Dream, and wondered what the author was trying to say about that.
Maybe you thought "Wow, this story is really sexist (or racist or ageist or classist); what's up with that?"
Maybe one of the characters intrigued you or reminded you of someone you knew.
Maybe you started wondering whether something that happened in the story was typical of the time period.
Maybe you noticed a recurring image like a window or a storm or a color and wondered why the author mentioned that.
To sum up, look for:
Once you have settled on something that interests you, go back and reread the story and make sure that you have taken note of all the places where that symbol, theme, character, or detail is mentioned or alluded to. Think about the connections and possible significance before you start reading about what other people thought of the story.