Irony can be found in a couple of different places in Act 4 of A Midsummer Night's Dream, especially situational and dramatic irony.
In situational irony, the reader or audience is surprised by the outcome of the story line or plot. Shakespeare makes use of situational irony when he has Titania give Oberon the foundling Indian boy because she has fallen in love with a man who has a donkey's head. In fact, this outcome is most ironic because the Indian boy is especially beautiful while Bottom with his donkey's head is particularly ugly. Despite Bottom's ugliness, we see Titania transfer her affections from the boy to Bottom, which is why she becomes willing to give the boy to Oberon. We see that Titania has fully transferred her affections when we see Oberon describe how she is treating Bottom in the lines, "For she his hairy temples then had rounded / With coronet of fresh and fragrant flowers" (IV.i.50-51). This description of crowning Bottom's head with flowers is nearly identical to the description of how she treated the boy, as we see in Puck's earlier lines, "...[b]ut she perforce withholds the loved boy, / Crowns him with flowers, and makes him all her joy" (II.i.26-27). Hence, we see that treating ugly Bottom in the same way she treated the beautiful Indian boy is an ironic situation.
In dramatic irony, the reader or audience knows far more about a character's situation or the unfolding action than the character actually does. We see Shakespeare relaying his use of dramatic irony when we see the lovers awake feeling disoriented while half believing what they have experienced was a dream and half believing it was real. This is an example of dramatic irony because the audience knows that what happened during the night was a result of fairy magic and their belief that it was a dream is also a result of fairy magic. We especially see the lovers feeling disoriented when they question whether or not they are actually awake. Demetrius phrases it best in his lines:
Are you sure
That we are awake? It seems to me
That yet we sleep, we dream. (IV.i.195-197)
Since the two couples believe that they are still sleeping and that they dreamed the whole experience while the audience knows differently, this is a perfect example of dramatic irony.