Saint Andrew was the brother of Saint Peter. Like Peter he was a fisherman. Like peter he was a disciple of Jesus. Like Peter he was the first bishop of a church, in this case in Byzantium (later Constantinople, later Istanbul). Like Peter he was martyred by crucifixion, and like Peter he said he wasn't worthy of being crucified in the same way as Christ. In Andrew's case, rather than inverting him, they turned the cross through 45 degrees to form the Saltire.
For a costume, I suggest carrying a large diagonal cross.