The easiest way to search for quotes from books is to perform a Google search by typing in the full quotation to find the reference. Another way is to use Bartleby, which has 120,000 authoritative quotations. Users of this website can search through Bartlett's Quotations, Harvard classics and anthologies, among other options, or by a number of specific authors, including H.G. Wells, Walt Whitman and W.B. Yeats.
Bartleby also has sections dedicated to Shakespeare, the Bible, Strunk, anatomy, nonfiction, reference books, fiction and poetry. Users of this website are also able to browse quotations, rather than search for them, by subject or popularity. This source is useful for more well-known quotations and may not be suitable for finding more obscure references.
For these, Google Book Search may be useful. At this website, users can enter quotations to view matching references. If the full quotation is known, it can be typed in quotation marks to let the search engine know to find the words in that exact configuration. If the quotation may have been paraphrased, leaving out the quotation marks will turn up references that are a close match. The book may not always be available, but users can nevertheless find out the source.