Explore the ways in which Shakespeare presents the supernatural in Macbeth

Shakespeare presents the supernatural in Macbeth in a variety of ways.
In the first scene of Act One, witches appear to not only introduce the element of the supernatural (that his Elizabethan audience would have enjoyed and believed in), but also to reveal the intense interest the witches have in Macbeth. Their lies (half-truths) will embolden him to murder his king, friend and relative, Duncan, and others in order to remain Scotland's new king.
The witches talk about their plan to meet Macbeth, which will ultimately take place in scene three.

THIRD WITCH:
There to meet with Macbeth. (8)

Before Macbeth kills Duncan, he sees the image of a dagger, which seems to lead him on to where his king is sleeping. He says:

Is this a dagger which I see before me, The handle toward my hand? (II.i.41-42)

When Duncan is murdered, the Great Chain of Being has been disrupted—the man God ordained (as they believed) to be the king has been removed from the throne. In doing so, Macbeth has disrupted the natural order of things, and unnatural and supernatural occurrences take place. Not only do smaller animals prey on larger animals, but Lennox reports hearing terrible sounds:

...as they say, Lamentings heard i’ the air,strange screams of death... (II.iii.56-57)

The supernatural is also introduced in Act Three, scene four, with the seeming element of madness in Macbeth, something that eventually will overcome Lady Macbeth. At the banquet after his best friend's murder, Macbeth sees a vision of the dead Banquo—which no one else can see:

MACBETH:
Thou canst not say I did it: never shake Thy gory locks at me. (62-63)

"Supernatural" refers to anything beyond the realm of the natural. It can be seen with the presence of the witches and their actions, in the strange occurrences in the world because of the disruption of order in the universe, and illusions and ghosts that present themselves to Macbeth.