Continuity mistake: When Kong lifts Ann from the bed she is wearing a short dress. In the close-up the dress goes way down to her ankles.
Continuity mistake: Kong breaks the window and Ann starts to shout and extends her right leg. A shot later it's bent downwards.
Continuity mistake: Kong breaks the window and takes Ann from bed. In the wide shot (where she's replaced by a stop-motion doll) she faints backwards. In the immediate close-up she is conscious and upright.
Continuity mistake: After Kong escapes from the theater, a car crashes against a wall with no glass on the windshield. In the next shot, broken glass appears.
Revealing mistake: At the Empire State, Kong extends his arm to grab the woman. Problem is, instead of catching her she magically flies up the air to his hand.
Revealing mistake: At the Empire State, the woman is an obvious square-shaped footage of film pasted on top of the footage of Kong. After the plane attacks Kong and his right arm goes limb it goes behind the pasted footage.
Answer: It's never shown or explained, and the film uses a broad "suspension of disbelief" premise. The audience just accepts the characters were able to somehow transport a huge ape to New York City.
raywest ★