The best way to find any quotations in literature, or any other area, is to simply use a search engine to find them. For example, if you were looking to find who spoke the following: "All the world's a stage, and all the men and women merely players: they have their exits and their entrances; and one man in his time plays many parts, his acts being seven ages," you would simply type it into the "Google" search bar. Once you hit enter, you will find multiple sites which denote the quote coming from William Shakespeare's play As You Like It. Some sites even offer the location of the quote and the meaning behind the quote.(In regards to the quote used in the example, it was spoken by Jaques to Duke Senior in Act II, Scene vii.) This is all found using a simple search.
As for sites which are helpful, they are linked under the references below.
The above answer to your question is right on. I have been surprised at how many quotations I have been able to trace just by typing them into Google. It hasn't even been necessary to put them into quotation marks. It is a marvelous time-saver. There are a number of websites accessible by just typing the word Quotations into Google or another search engine. These give you quotations by subject, quotations by author, etc. I have found it interesting to look up all available quotations by a particular author (e.g., Freud, Goethe, Aristotle) to get an overview of the author's thinking and personaliity.