It appears as a circular tower, made either of Cobblestone, Moss Stone (in swamp-like biomes), Sandstone (in deserts), Stone Bricks (in mountains) or Terracotta (in Mesas), and has 4 different designs (short, medium, tall and branched). At the top is a pointy roof made out of a random color of Terracotta.
Inside is a spiral staircase leading up to a small room containing an Arcane Workbench, 12 Bookshelves and a Wizard. Some towers will instead contain an Evil Wizard and will have one of their Bookshelves replaced with a Chest containing loot.
A naturally spawned Wizard Tower.
A Wizard at the top of a Wizard Tower, wearing Ice Mage Robes.