In order to play local multiplayer, you need to have different user accounts on your Wii U.  Here's how you get everything working:

  1. Create a new Wii U local profile - instructions here:
  2. Start Terraria with the new local profile and create a character
  3. Quit Terraria, switch back to the first profile, and start Terraria again
  4. Open your world, press '+' on the second player controller, and the second profile should display
  5. From there, you can select any character on the second profile and start playing!