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:

In A Room with a View E. M. Forster writes, “[C]hoose a place where you won’t do very much harm, and stand in it for all you are worth, facing the sunshine.”

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:

In A Room with a View E. M. Forster writes:

The sun rose higher on its journey, guided, not by Phaethon, but by Apollo, competent, unswerving, divine. Its rays fell on the ladies whenever they advanced towards the bedroom windows; on Mr. Beebe down at Summer Street as he smiled over a letter from Miss Catharine Alan; on George Emerson cleaning his father’s boots; and lastly, to complete the catalogue of memorable things, on the red book mentioned previously. The ladies move, Mr. Beebe moves, George moves, and movement may engender shadow. But this book lies motionless, to be caressed all the morning by the sun and to raise its covers slightly, as though acknowledging the caress.

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.”

In MLA style, sentences following a colon usually start with a lowercase letter, but it is acceptable to start such sentences with a capital letter. Thus, by using whatever you find in the source, you can maintain the integrity of the quotation and avoid using brackets unnecessarily.

Integrated into Your Syntax

A quotation that is integrated with the syntax of your sentence begins with a lowercase letter: 

Lucy realized that “even men might suffer from unexplained desires, and need help.”

If the first letter of the first word you quote is capitalized in your source, use a lowercase letter enclosed in square brackets:

Lucy caught her cousin’s eye, and “[s]omething in its mute appeal made her reckless.”

A block quotation begins with a lowercase letter if it integrally continues your introductory wording:

In observing George’s reaction, Lucy concludes that

men were not gods after all, but as human and as clumsy as girls; even men might suffer from unexplained desires, and need help. To one of her upbringing, and of her destination, the weakness of men was a truth unfamiliar, but she had surmised it at Florence, when George threw her photographs into the River Arno.