How can I talk about representations of madness in The Turn of the Screw?
You could definitely make a case for insanity in terms of the governess. Insanity is a them in this novel. The question of whether the governess is actually seeing the ghosts or hallucinating in an insane state is worth exploring. She is the only one to publicly admit to seeing the ghosts. No one else claims to see anything out of the ordinary.
She believes the truth is finally evident when the ghost of Miss Jessel appears while the governess and Mrs. George are together. She is excited until she realizes that the housekeeper sees nothing. This is one example to use with regards to the ghosts, insanity, and illusions.
You can also use the time she spends awaiting the appearance of the ghosts in which she questions her own sanity. She waits weeks and thinks she should be relieved that they no longe3r appear, but she does not stop looking for them.
I know what you mean because recently I was assigned to argue the book as a case of insanity and I could only see the ghosts. But after speaking with the other members in my group I can now see it the other way.
The most important thing (I think) to concentrate on to would be her motives for imagining the ghosts and their possesion of the children (this assumes that imagining ghosts would be classified as insanity). She originally sees the children as completely perfect (an assumption based almost entirely on their beautiful outward appearance, another theme in the book) so when they begin to misbehave she immedeately jumps to the conclusion that it must be the fault of their previous caretakers. If you really look at it, all the children's antics that she blames on possesion and coercion by the ghosts are really the actions of normal children acting out.
Another cause of her "hallucinations" is her sexual frustration/hysteria. She believes herself in love with the master and her first vision of Peter Quint is after she fantasizes about meeting the master in the garden.
There's lots more to be said and much more evidence, but these are the main themes and causes.
Hope this helps!