Whether to capitalize or lowercase the first letter of the first word of a quotation depends on how the quotation is integrated into your prose and what appears in the original.
After a Verb of Saying
Capitalize the first letter if the quotation appears after a verb of saying, regardless of the case used in the source–but flag any alterations you make.
A quotation that follows a verb of saying (e.g., writes, says, states, exclaims) and is run in to your text is introduced with a comma and begins with a capital letter. If the first quoted word begins with a lowercase letter in your source, use a capital letter enclosed in square brackets to indicate that you’ve altered the source:
Introduce a block quotation that follows a verb of saying with a colon, and capitalize the first letter of the first word of the quotation:
After a Colon
A quotation that is run in to your text and introduced with a colon may begin with a lowercase or capital letter—use whatever you find in the source:
Forster describes George’s reaction to the memory: “he blushed and was ashamed.”
George’s reaction provokes in Lucy an observation about the weakness of men: “Perhaps anything that he did would have pleased Lucy, but his awkwardness went straight to her heart; men were not gods after all, but as human and as clumsy as girls; even men might suffer from unexplained desires, and need help.”
Integrated into Your Syntax
A quotation that is integrated with the syntax of your sentence begins with a lowercase letter:
If the first letter of the first word you quote is capitalized in your source, use a lowercase letter enclosed in square brackets:
A block quotation begins with a lowercase letter if it integrally continues your introductory wording: