Perseus is often portrayed in art carrying the head of Medusa in his hand – easily recognizable by the snakes growing instead of hair – and with his head turned and eyes shut, to avoid the gaze that turned everybody into stone. This posture captures the image of the hero after Medusa was killed, when he was using her head as a weapon against his enemies – and there was no shortage of those, as Perseus had to petrify both his father in law, Cepheus, father of Andromeda, and his accomplices, and the ruler from his adoptive homeland of Seriphos, a king named Polydectes. After that, Perseus gave the Medusa head as an offering to the goddess Athena, and she attached it to her shield, and it became part of her imagery ever since (you can read more about that in The Symbols of Athena).
Another symbol of Perseus is a borrowed one – the cap of invisibility, taken from Hades only for the duration of his adventures. The cap covered its wearer into a cloud so dark it was practically invisible – and Perseus used it to escape the wrath of Medusa’s sisters.
In paintings and on pottery you might also recognize Perseus since he’s accompanied by Athena and Hermes – the two gods who protected and helped him during his trials.
If portrayed as an infant, Perseus is depicted together with his mother, Danae, locked in a box – which was either an underground chamber made of bronze, where they were imprisoned by Danae’s father, or the wooden box in which the two were thrown into the sea to die. The image was extremely popular during the classical antiquity, and was revived by artists during Renaissance, though they focused more on Danae and the moment when she was seduced by Zeus, in the form of a golden shower – thus before the birth of Perseus.