The most basic way in which Virgil reveals the personalities of his characters is through their actions. For example, when we see Aeneas fighting to save Troy and then carrying his father to safety on his back, we can tell that he is a brave warrior and citizen, and devoted to his family. At other times, actions can raise questions. What does it mean, for example, when Aeneas kills the surrendering Turnus in Book 12? Although actions are a basic way of revealing character, their meanings are sometimes far from obvious.
Although this doesn't come up that often, Virgil can use what characters wear to reveal what's going on inside their heads. For example, when the god Mercury comes down to earth and sees Aeneas all dressed up in fancy Carthaginian clothes, that's a clear sign that his fling with Dido has distracted his attention from his primary mission.
The most common form of direct characterization in the Aeneid is the fixed epithet. This device, which Virgil picked up from Homer, just means you come up with some word that describes a character, and then use it to reference them over, and over, and over again. The most obvious use of this device in the Aeneid is the adjective "pious" attached to Aeneas.
Another way in which characters are revealed in the Aeneid is their relationships with their family members. For example, we learn a lot about Aeneas from the devoted way in which he treats his father, and from how he tries to set a good example for his son Ascanius. In contrast, Turnus only really starts thinking about his own father when he needs an excuse for preserving his own life – telling Aeneas to spare him so he can see his old man Daunus again. This contrast helps reveal our understanding of Aeneas as a responsible character who cares about others, versus Turnus as an irresponsible character who only cares about himself.
The rustic surroundings of the Arcadians play into the forthright character of Evander and his son Pallas. In contrast, the city-dwelling Latins are portrayed as shifty and untrustworthy.