Depends on the library.
Most public libraries have separate fiction and nonfiction sections, and the fiction is organized alphabetically by "main entry." Roughly speaking, the main entry is the author's last name if there is one, or the title if there isn't (collections of short stories, for instance, have a title main entry).
Some libraries have separate sections for genre (mystery, romance, science fiction) and organized alphabetically by main entry within the genre.
Most academic libraries in the U.S. do not have separate fiction and nonfiction collections, and fiction is shelved together with nonfiction in the "literature" classes.
In the Library of Congress Classifiction, the literature classes are from PA-PT. Here you'll find fiction classed by language, then by country of origin, then by time period, then alphabetically by author's last name. Fiction books are shelved together with other literature (poetry, drama, essays) and with works of literary criticism.
Chances are, if your library uses Dewey then it has a separate fiction section. This gives people the mistaken notion that this arrangement is according to Dewey. In fact Dewey has classes for fiction, and some libraries -- Oklahoma State University Library being one -- use them.
In the Dewey Decimal system, literature is in the 800's, arranged by language (with separate sections for American and English literature). Dewey Decimal, unlike LC, arranges literature by form, and numbers for fiction end in "3", e.g.:
813 American fiction
823 English (non-U.S.) fiction
833 German fiction
843 French fiction
Finally, even if your library has separate fiction and nonfiction sections, it may still shelve some classic fiction or foreign-language fiction in nonfiction. Check with your librarian for details about your library's policy.