I've googled this, and found conflicting answers. Should the title of a short story be italicized or put in quotes?
It will be both in the title and the body of a paper discussing the story.
In a serious essay or academic paper I would put any book title, whether fiction or non-fiction, or the title of any journal article, in italics. The name of the author should not be italicised. Publishing date and details usually go in brackets. So in the body of the text you could say something like:
In his study of camels which sleepwalk across the deserts of Arabia, G.K. Johnson in his book Do camels dream? refers to work he did in 1986.
The footnote might read Johnson G.K. Do camels dream? (London 1987).
Edit. This works for short stories assuming the short story concerned is the only content of the publication. If one is referring to a story from a book of short stories, then quotation marks rather than italics would be used, and there is a further system for referencing this. However I apologise that I may have got out of my depth on this as it is several years since I was writing academic essays.