Dramatic irony is created when the audience knows more than a character. In act 3, scene 1, the king and Polonius have concocted a plan whereby Hamlet will "accidentally" run into Ophelia, while Claudius and her father hide and watch their interaction, to see if unrequited love for Ophelia is truly the cause of Hamlet's madness. See lines 35–40. First, then, they think his love for Ophelia might be the cause of Hamlet's behavior; we know that it is not. Second, we know that they plan to listen to the young couple's conversation, unbeknownst to Hamlet (though he may guess at it). Both are examples, then, of dramatic irony.
Verbal irony is created when a character says the opposite of what they mean. Hamlet employs verbal irony when he taunts Ophelia before the play in act 3, scene 2. When she calls him merry, he says,
O God, your only jig-maker. What should a
man do but be merry? For look you how cheerfully
my mother looks, and my father died within 's two
Hamlet is not merry at all, and he certainly does not believe that the only thing a man can do is be merry. He proclaims that he is God's "jig-maker" or comic, but he more likely means that he is like a fool.
Hamlet uses disease imagery in his conversation with his mother in act 3, scene 4. He says,
Sense sure you have,
Else could you not have motion; but sure that sense
Is apoplexed; for madness would not err;
Nor sense to ecstasy was ne'er so thralled,
But it reserved some quantity of choice
To serve in such a difference. What devil was 'it
That thus hath cozened you at hoodman-blind?
Eyes without feeling, feeling without sight,
Ears without hands or eyes, smelling sans all,
Or but a sickly part of one true sense
Could not so mope? (3.4.81–91)
Hamlet refers to apoplexy, a kind of physical paralysis (saying that his mother's "sense" has become unable to function correctly); he insists that her sense has become a slave to madness (or "ecstasy"). Then he describes her as "blind" and insists that her senses are not all working in concert. She might see but not feel, or feel but not see, hear without being able to feel or see, or smell alone. Here, he employs several types of imagery to character what he sees as his mother's disease.