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If your talking about Ocarina of time, to leave on your own the exit is a door right in the gate in there is a ladder, I personally just get caught intentionally, also if its your first time, just talk to zelda and her caretaker will escort you (warp with you to out of the castle/town pretty much)

(spirit tracks) just keep going down its where you came in when you first came to get your engeneers certificate