Commas set off a quotation from words used to introduce or identify the source of the quotation. A comma following a quotation goes inside the closing quotation mark. (See 44d for advice about using colons instead of commas to introduce quotations.)

Do not use a comma after a question mark or exclamation point.

Do not use a comma when you introduce a quotation with that.

Do not use a comma before an indirect quotation—one that does not use the speaker’s exact words.