Capitalize the first word in a quotation if the quotation is a complete sentence or if it is an interjection, an incomplete question, or fragmentary response.
Correct: He said, “Why did you come back?”
(Quotation is a sentence by itself.)
Incorrect: She replied, “you wanted me to.”
(A fragmentary response, you needs a capital.)
A quotation is not capitalized if it is not a complete sentence and is part of the larger sentence.
Correct: I believe it was a “far, far better thing” to have confessed the crime.
(This quotation from Dickens is part of the larger sentence and is not a complete sentence in itself.)