Titles of individual short stories and poems go in quotation marks. The titles of short story and poetry collections should be italicized. For example, “The Intruder,” a short story by Andre Dubus appears in his collection, Dancing After Hours.
This can get a little tricky when authors title their collection after a story within that collection. Junot Diaz’s collection of stories Drown includes a story titled “Drown.” In this case, the use of italics or quotation marks can help the reader understand what’s being referenced—the entire book or the individual story.
This usage remains true even when titles appear within quotations. Let’s say you write a poem about a poem and you title it this way:
Lines after Reading “The Love Song of J. Alfred Prufrock”
Now, you need to enclose the entire title of the poem within quotations when you mention this poem in a cover letter. The title that appears within the title, then, should be enclosed in single quotation marks:
“Lines after Reading ‘The Love Song of J. Alfred Prufrock’”
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.