Quotation marks are primarily used to show exact language written by someone other than the writer, including designating speech. Quotations marks always come in pairs and are used in direct quotations but not indirect quotations.
Direct quotations use another person's exact words. The quotations marks come at the beginning and the end of the other person's words. The first letter of a direct quote should be capitalized unless the quoted material is a fragment of a complete sentence. If a direct quote is interrupted in the middle of a sentence, the second part should not be capitalized. For example, "'I didn't see an actual alien being,' Mr Johnson said, 'but I sure wish I had.'" Punctuation goes inside the quotation marks. If a quotation contains a spelling or grammar error, the error should be transcribed exactly and follow with a "sic" in brackets to indicate that the mistake is not the writers.
An indirect quotation is a paraphrase or summary of another person's words and does not require quotation marks. Direct quotation should be used when the quote contains language that is particularly striking, like in a speech by Martin Luther King Jr. Direct quotations should also be used if the quoted author is using a unique term they have coined themselves.