Colons introduce quotations that are formal or lengthy.

Correct: Dickens wrote: “It was the best of times, it was the worst of times.”
(Formal quotation)

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.