The rules of citation that apply to academic and research papers don't apply to novels. You don't need to include a bibliography, and footnotes aren't necessary unless you're using them for some literary purpose, à la David Foster Wallace. However, it is important to acknowledge the sources you relied on for research. Novel writers do that in their acknowledgements, a notation that appears in many novels, either in the front matter or at the end of the book.
The acknowledgements section is an opportunity to thank those people and organizations that helped make the book possible, like agents, editors, granting institutions, and family members. Great sources of research fall in this category, too. You don't have to name each and every source, though. For The Shipping News, Annie Proulx consulted hundreds of sources and singled out only the ones she found most instrumental. In her acknowledgements, she cites books like Clifford W. Ashley's The Ashley Book of Knots, which provided inspiration, and S.A. Gordon's Folk Music in a Newfoundland Outport, for “contain[ing] information difficult to discover elsewhere." Research isn't just confined to books, of course. One of Proulx's most exuberant acknowledgements goes to Bella Hodge, “who suffered dog bite on my account and showed me the delights of Newfoundland home cooking."
If you're quoting directly from previously published material, like a book or a song lyric, you need to secure permission to do so. (Consult a lawyer familiar with these sorts of permissions. The laws vary by medium and are open to interpretation.) The citations for these permissions usually appear on the copyright page of the book.