Science Fiction and Fantasy has a highly active story-identification tag but where should I ask for identification of fictional stories that are of neither science-fiction nor fantasy genre?
The Literature Stack Exchange proposal mentioned in Wrzlprmft's answer has been in public beta since early 2017 and does indeed accept story identification questions. These questions should be tagged
identification-request and must fulfil a number of criteria, which are described in the tag wiki:
A list of details one should consider adding to their question includes, but is not limited to:
When did you read the story, and how old was it?
Did you read it 10 years ago? Last summer? "When I was in high school" is not descriptive. Try to provide a year range instead. Was it an old crumbling book or a fresh one? Did you see it in a magazine from the 1980s or on a website yesterday?
Medium and appearance
What did the cover look like? Was it a thick book? A magazine? Short story collection? Novel? Maybe printed in a textbook? Was it an online story?
What language did you read it in, and was it translated?
What language did you read the book in? This helps to narrow down the possibilities. In case you read a translation, you should also try to provide the original language the book was written in - this will significantly narrow down the search area.
Where did you read this story?
Public library? Airport book shop? USA? Italy? Any of these will help.
Every little detail will help - do not omit anything just because you think it is insignificant. Even details that you are unsure of can be included, just with a disclaimer that you are unsure about them.