The best quotes come directly from either the source material, or from a respected critic/writer and are highly relevant to the subject at hand. For example, if you're writing about Animal Farm, you're going to want to use direct quotes from the text that help prove your thesis. Alternately, you can use quotes from the author, George Orwell, himself or from respected critics of the work.
Here on enotes.com, many of the books covered have a quotes section. Here are some examples:
When looking for a critical essay to quote from, make sure it's by a recognized critic and not just a student essay that's been posted online. On enotes, you can find critical essays both within the topic, or inside the author topic. For example, here are some critical essays about George Orwell:
While there are many websites that contain quotable quotes, such as www.brainyquote.com or www.quotablequotes.imgfave.com, the student can just type in whatever type of quotation he wants on one of the search engines; for example,
Quotation about responsibility
In addition, there are books of quotations that are available at large book stores in malls; these are arranged by types. One large quotation book will have quotes according to subjects and, often, according to famous authors such as Shakespeare.
Many readers prefer to keep their own notebooks in which they record passages from works that they themselves read and find moving, arranging them according to authors, or subjects, etc. When they wish to use these passages or lines, the quotations are handy, then. It is a good idea to store quotes from fiction as well as non-fiction. For, there is a wealth of thought from such writers as American Transcendentalists Ralph Waldo Emerson and Henry David Thoreau; great British thinkers such as David Hume, John Stuart Mill, Charles Darwin, Winston Churchill, and powerful writers such as William Shakespeare Charles Dickens and Thomas Hardy; French philosophers such as Voltaire, Jean-Jacques Rousseau, Montaigne, Montesquieu, Descartes, and others. Indeed, reading "doth make a man full," as Thomas Jefferson stated. So, the more that a student reads, the richer he becomes with ideas and meaningful thoughts, many of which can be utilized later in his own writing.
Very often, I advise my students to begin their essays with a relevant quote, but, as you have noted, the hard part can be finding the appropriate quote. A good place to start is by going into any browser search engine and typing something like "quotes about...." Obviously the ellipsis (...) means to add your subject matter such as, "Quotes about friendship."
As for particular sites, a site I find useful is http://www.brainyquote.com. On this site, you can search by the name of a person you are hoping to find a quote from, a topic, a theme, etc.
Also, don't overlook quoting the dictionary. This is particularly useful when you are writing about a literary term. For example, if you were writing about theme, you could begin by saying, "According to dictionary.com, theme is defined as, 'A unifying or dominant idea, motif, etc., as in a work of art.'" Using this technique, when all else fails, will provide you with a quote, and it also establishes a definition for the term from a verifiable or academic source. It essentially says to your reader that you are writing based on an academic understanding of the term rather than your own knowledge, memory or experience. Now, you may be VERY intelligent, and your personal definition may be approaching perfect, but quoting "experts" always adds credibility to your writing, and using the dictionary in this manner does just that. Oh, and print copies of the dictionary work just as well.
Hope this was helpful. Quote away!
If you need quotes from a specific work you are studying, the ideal thing to do is think ahead and highlight key passages as you go. However, when that isn't possible you can sometimes garner the information from online resources such as the etexts tab here on eNotes. Simply, find the work in question and use the summary tab to estimate where in the book you should look for a specific quote. (Note that this method requires being somewhat familiar with the text beforehand). You could also just as easily search "Quotes from (novel, character, or author)" and see if that renders the results you need.