In Romeo and Juliet, how does Shakespeare use dramatic irony in Act 2 Scene 2 (the balcony scene)?

This is a great question! Remember the definition of
dramatic irony: dramatic irony is defined as when someone on the stage and/or the
audience knows something that one or several of the other characters do not. One of the
essential elements of dramatic irony in this play over all is of course the tragic end,
when we know that Juliet is just about to wake up, but Romeo doesn't, and goes on
killing himself, just before Juliet revives.

However, when
we think about dramatic irony in this famous scene, one place to start is towards the
beginning. Remember that Romeo and Juliet have just had rather a sudden and quick
meeting before Juliet is dragged away. Therefore Romeo is left wanting to have some
confirmation of what he is experiencing and that he is not
dreaming.

He receives this confirmation in the form of
Juliet appearing on the balcony and addressing "Romeo," ironically not knowing that he
is actually there to hear every word. Listen to what she
says:

O
Romeo, Romeo! Wherefore art thou Romeo?

Deny thy father and
refuse thy name;

Or, if thou wilt not, be but sworn my
love,

And I'll no longer be a
Capulet.

This is enough to
give Romeo the confirmation that his feelings are mutual and shared by Juliet, and he
ponders in an aside whether he should reveal his presence at this stage or wait to hear
more. Therefore this is dramatic irony because we know that Romeo is actually there,
hearing every word that Juliet is actually addressing to Romeo, though she doesn't know
where he is.