Several Internet websites like QuotationsPage.com and QuoteInvestigator.com have search tools that allow you to search for the author of a quote. Your local library may have books listing famous quotes and their authors, as would some book stores.
Internet websites are the fastest and easiest way to search. To do website searches, enter a bit of the quote or the entire quote you wish to trace to its author in the search box on the search page. If you suspect a certain person may have authored a quote, you can use the search box to reverse search the author's name.