To complete your assignment, you'll first want to gain a good understanding of possible interpretations of Antigonus's "Come, poor babe" speech in Act 3, Scene 3. To do that, you'll want to read through literary criticism on Shakespeare's The Winter's Tale, focusing on criticism of Act 3. Literary criticism can be difficult to find online, though eNotes does have a couple of articles. Your best bet is to find literary criticism in your school library, especially the library's databases for scholarly articles. One thing critics like Jack A. Vaughn point out in the article titled "Overview" found on eNotes is that Act 3, Scene 3 marks a real turning point in the story. Up to Act 3, Scene 2, we have what is a traditional Greek tragedy, but that tragic ending ceases when in Scene 3 the baby is rescued by the shepherd. Hence, Act 3, Scene 3 marks a transition from a tragedy to a comedy. Vaughn especially sees Antigonus's "poor babe" speech as transitional because it no longer contains the same language as in the first 2 acts but instead now contains "fanciful and extravagant language," representing a shift to a lighter tone ("Overview"). Vaughn asserts that we can see fanciful language being used when Antigonus describes seeing Hermione in a dream, dressed in "pure white robes" like an angel or a ghost and "gasping to begin some speech." Antigonus even ends by describing her as giving "shrieks" and then disappearing into thin air, which also adds to the fantastic vision. Hence, the fanciful language helps characterize the tone of Act 3, Scene 3, as well as the tone of Antigonus's speech, as the same lighter, less serious tone found in a comedy; in short, based on Vaughn's interpretation, this is not a serious, dramatic scene in the way that scenes are serious and dramatic in tragedies.
Once you figure out what interpretation you want to go with after looking over a few, you next want to decide how the actor should play the part. For example, if one were to go with Vaughn's interpretation that the speech represents a transition in tone, then one would not have the actor playing the part speak the lines in a terribly serious way, the same way an actor might say lines to speak of a tragic death. Instead, the actor might add drama and gesticulations to express either awe or terror and to add to the fantastical mood while describing things like the vision of Hermione, the same way an actor might describe having seen a ghost, such as how in the very first scene Marcellus and Bernardo speak of seeing the ghost of King Hamlet in Shakespeare's Hamlet. For example, the actor might begin showing awe in his voice when he starts describing his vision while saying, "[T]hy mother / Appear'd to me last night, for ne'er was dream / So like waking." He might even begin to express terror when he quotes Hermione's vision as saying that for abandoning the child, Antigonus "'ne'er shalt see / Thy wife Paulina more.'" However, we must also remember that this is a very sorrowful moment in the play, so the actor will also speak in a voice that portrays devastating sorrow when speaking to the baby in the opening lines or when describing the vision's command to "weep" while he leaves the poor baby crying. Reading further literary criticism will give you further ideas.