How do I write a literary essay about how Macbeth's hallucinations (such as the prophecies and dagger) affect him and his behavior?

The first important thing you need to remember in writing a literary essay is that it has to be formed around a thesis statement.  Your thesis comes from your topic.  In this case, you want to write about the cause and effect of the hallucinations, or how Macbeth’s fear and guilt lead him to act hastily.  It does partly depend on what you think is a hallucination.  Are the witches real?  In your case, you might want to argue that they are not, based on what your teacher said.

Your thesis might be something like this.

Driven by guilt and fear, Macbeth allows his hallucinations to guide him to hasty and unwise actions.

An example of this, of course, is the witches’ first presentation to Macbeth that he would be king. Your teacher presents the witches’ prophecies as part of the hallucination. Banquo was there too, but that doesn’t mean that Macbeth didn’t hallucinate this reaction.  Macbeth at first seems disturbed by the witches’ words.

Third Witch

All hail, Macbeth, thou shalt be king hereafter!

BANQUO

Good sir, why do you start; and seem to fear
Things that do sound so fair? I' the name of truth,
Are ye fantastical, or that indeed
Which outwardly ye show? (Act 1, Scene 3)

You could argue either that Banquo is part of the hallucination or that he was reacting to something else.  Either way, Macbeth has a strong reaction to the prophecies. He seems to go from being a loyal solider to deciding he wants to be king, whatever the cost.  Notice that you need to use quotations to support your arguments in a literary essay, such as I did here.  Think of it as a persuasive essay where the support is textual evidence.

A second significant hallucination has Macbeth alone.  He is trying to decide what to do about Duncan and sees an imaginary dagger floating in the air. He takes this as a sign that he does need to kill the king.

Is this a dagger which I see before me,
The handle toward my hand? Come, let me clutch thee.
I have thee not, and yet I see thee still.
Art thou not, fatal vision, sensible
To feeling as to sight? or art thou but
A dagger of the mind, a false creation,
Proceeding from the heat-oppressed brain? (Act 2, Scene 1)

Macbeth is again spurred into action by this hallucination.  He dithers about whether or not to kill Duncan, but he considers this dagger as evidence that he was meant to kill Duncan to become king.  As you explain the meaning of the dagger, be sure to use this quote or another part of it as evidence.

Perhaps my favorite example of a hallucination is Macbeth’s seeing Banquo’s ghost at the dinner party. 

MACBETH

The table's full.

LENNOX

Here is a place reserved, sir.

MACBETH

Where?

LENNOX

Here, my good lord. What is't that moves your highness?

MACBETH

Which of you have done this? (Act 3, Scene 4)

This manifestation of Macbeth’s guilt results in the party ending quickly with Lady Macbeth making excuses for her husband. Yet the ghost demonstrates that Macbeth is driven by guilt as well as ambition. This will influence his actions from here on, but he has felt guilty since killing Duncan.  He begins to suspect everyone and everything, and it leads to his downfall. He kills Macduff’s entire family, but is unable to kill Macduff, and he makes an aggressive and foolish last stand against Malcolm’s army.