Craft an Iron/Lead Anvil
Reach Hardmode by defeating the Wall of Flesh
Get Souls of Flight from Wyverns in the Sky/Space layer
Get Souls of Light or Souls of Night from their respective biomes
Get Pixie Dust from Pixies in the Hallow
Get Feathers from Harpies
Buy a Flight-related item from the Witch Doctor, Steampunker, or other relevant NPCs if available
Use the required materials at a Mythril/Orichalcum Anvil or Iron/Lead Anvil, depending on the wing type
Equip the crafted wings in the accessory slot