Macbeth's mental deterioration begins when he kills King Duncan and continues as he gradually becomes a ruthless murderer, while Lady Macbeth's mental decline is the most conspicuous in Act 5 in the famous sleepwalking scene.

Firstly, let us focus on Macbeth's hallucinations. His ambition to murder Duncan so that he could become the king proves to have a very detrimental effect on him. Although he achieves his dream of becoming the ruler of Scotland, he loses his inner peace and stability for good. This is evident in the scenes when he appears to behold certain objects and apparitions, such as the invisible knife, the ghost of Banquo, etc. Here are some of the quotes that demonstrate Macbeth's descent into insanity:

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?

In this quote, Macbeth is tormented by the vision of an invisible dagger as a result of his guilty conscience. As he gets involved in killing more people who he thinks could imperil his position, his insanity only intensifies:

Prithee, see there! behold! look! lo!
how say you?
Why, what care I? If thou canst nod, speak too.
If charnel-houses and our graves must send
Those that we bury back, our monuments
Shall be the maws of kites.

In this scene, which is also called "the banquet scene," he sees the ghost of Banquo, whose assassination he ordered. Every guest is startled by Macbeth's reaction, and the scene implies that Macbeth's condition will only worsen.

As far as Lady Macbeth's mental decline is concerned, she becomes an irrelevant character once Macbeth gains power. Macbeth neglects his wife because he is obsessed with maintaining his status as the king of Scotland, so his wife no longer interests him. This reflects badly on her health, as we see in Act 5, when she is tortured by her guilt-ridden conscience:

Out, damned spot! out, I say!—One: two: why,
then, 'tis time to do't.—Hell is murky!—Fie, my
lord, fie! a soldier, and afeard? What need we
fear who knows it, when none can call our power to
account?—Yet who would have thought the old man
to have had so much blood in him.

She cannot forget about her involvement in the murder of Duncan, and her loss of inner peace proves to be too much for her to handle.

Good question.

To prove Macbeth's insanity, look at when he sees things no one else does like in Act 2 scene 1:

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...

And later in Act 2 scene 1:

I see thee still,
And on thy blade and dudgeon gouts of blood,
Which was not so before.

And the ghosts…
Also, when he hears things no one else does:

Me thought I heard a voice cry “Sleep no more!
Macbeth doth Murder sleep”—the innocent sleep,

To prove Lady Macbeth's insanity, look at when she tries to rub the (invisible) blood from her hand in Act 5 scene 1.

To prove both, look at all the times they change emotions or positions quickly.