If you're looking for a specific story, titles might not be consistently indexed. Look for titles of collections that the story could be in. Remember that anthologies often contain stories from multiple authors across a specific theme.
Google Books is a great place to search if you remember a specific line or phrase but not the title or author.
The Dictionary of Literary Biography, found in Artemis, can help you remember titles by specific authors.
Short Fiction
The Best American Short Stories 2013 by Elizabeth Strout; Heidi Pitlor (Editor)
Call Number: PZ1 .B446235 2013
ISBN: 0547554834
Publication Date: 2013-10-08
An annual collection of the best short stories from American authors in the past year, the library holds this collection back to 1978.
Short fiction criticism; a checklist of interpretation since 1925 of stories and novelettes (American, British, Continental) 1800-1958 by Jarvis Thurston
Call Number: Z5917.S5
Publication Date: 1960
The Facts on File Companion to the American Short Story by Abby H. P. Werlock (Editor)
Call Number: PS374.S5 F33 2000
ISBN: 0816031649
Publication Date: 2000-02-01
"A handy volume that presents an immediate introduction to American short fiction from the 19th century to the 1990s, the 675 alphabetically arranged entries consist of author biographies, literary terms, theories, themes, well-known characters, influential events, and summaries of major stories. Entries are definitive and written in a clear style."--"Outstanding Reference Sources," American Libraries, May 2001.
The Best American Short Stories 2013 by 
Short fiction criticism; a checklist of interpretation since 1925 of stories and novelettes (American, British, Continental) 1800-1958 by 
The Facts on File Companion to the American Short Story by 