Ellipsis dots [ . . . ] indicate material left out of a quotation.
An ellipsis consists of three spaced periods. Always put one space before, after, and between them: [ . . . ]. Do not bunch them together like this: […].
Readers will assume that some material comes before and after the sentence you’re quoting. Therefore there is no need to place ellipsis dots at the beginnings and ends of quotations:
Displaying his prodigious knowledge of English grammar, David Foster Wallace opines: “Hopefully at the beginning of a sentence . . . actually functions . . . as a ‘sentence adverb’ that indicates the speaker’s attitude about the state of affairs described by the sentence” (100-01).
And Hopefully at the beginning of a sentence, as a certain cheeky eighth-grader once pointed out to his everlasting social cost, actually functions not as a misplaced modal auxiliary or as a manner adverb like quickly or angrily but as a “sentence adverb” that indicates the speaker’s attitude about the state of affairs described by the sentence (examples of perfectly OK sentence adverbs are Clearly, Basically, Luckily), and only SNOOTs educated in the high-pedantic years up to 1960 blindly proscribe it or grade it down.
— Consider the Lobster and Other Essays
When the ellipsis coincides with the end of a sentence, mark the end of the sentence with a period before inserting the ellipsis:
Robert Kaplan draws a contrast between Nevill Chamberlain and Winston Churchill: “Chamberlain’s was a shallow realism. . . . But Churchill knew more” (18).
Chamberlain’s was a shallow realism. He knew his people wanted peace, and their money spent on domestic needs rather than on armaments, so he gave them these things. (When Chamberlain returned from Munich after appeasing Hitler, he was proclaimed a hero.) But Churchill knew more.
— Warrior Politics
When the ellipsis comes before the end of one sentence and the start of another, place the period after the ellipsis, skip a space, and begin the next sentence:
Andrew Sullivan points out the ubiquity of friendship: “For, of all our relationships, friendship is the most common . . . . In its universality, it even trumps family” (176).
For, of all our relationships, friendship is the most common and the most universal. In its universality, it even trumps family.
— Love Undetectable