The mood is extremely ominous in The Turn of the Screw. This largely comes from the sheer amount of foreshadowing. It actually takes quite a while for the narrative to get to the moment in which the governess first sees the ghost of Peter Quint, and this delay just creates a building sense of anticipation.
The frame narrative contributes to this tense mood—not only does Douglas insist that he has a harrowing story, but he makes his listeners (and, in turn, readers) wait two days to actually hear it, since he sends for the governess's manuscript. Then, once he starts reading the governess's manuscript aloud, he has to get through the initial stages of the narrative, meaning that the suspense continues to mount for quite a while. And even then, when the governess finally sees the first ghost, the details are quite ambiguous. It's unclear even to the governess what, exactly, she has seen. This only makes the mood all the more foreboding.
Finally, the narrative's extremely ambiguous culminating scene is especially unsettling, as the governess's story has posed more questions than it has answered. By the end of the novella, it's no longer clear whether or not the governess is mentally sound, and this kernel of doubt retrospectively makes the mood of the entire novella feel suspicious and unnerving.
