It's all about the PoV. You can keep tons of things secret, so long as they're secret from the person whose eyes we're sharing. For instance, in the Sixth Sense (and bear in mind I've never seen this movie, but I get the gist), the key in the novel would be to have the PoV perhaps from the shrink (but allow the shrink to not know he's dead). Follow him as he treats the boy, as he tries to interact with that woman in the movie. From his point of view, we'd only understand that this woman isn't interested in talking to him, and it would eventually lead up to an emotional climax where he would realize he was dead and, in turn, so would we.
So really, it's all down to the PoV. You can't delibrately lie to the reader...the reader likes to be able to, after the twist was revealed, go "oh yeah! I can see where that came from!" They want to know there was buildup for it. You have to pick a POV that doesn't have all the answers, that is able to wrongly interpret all this clues to the reader (but in a way that is justifiable to his or her mind), so that when the truth is revealed, you can see how the character made the wrong assumptions.