Colons introduce quotations that are formal or lengthy.
Correct: Dickens wrote: "It was the best of times, it was the worst of times."
Colons introduce quotations that do not begin with a "he said/she said" clause.
Correct: Alexandra took the microphone: "Your honor, I object."
(Clause preceding quotation does not have a verb which denotes speaking.)
In all cases, the colon precedes the quotation marks.