In order to play local multiplayer, you need to have different user accounts on your Wii U. Here's how you get everything working:
- Create a new Wii U local profile - instructions here: http://en-americas-support.nintendo.com/app/answers/detail/a_id/1716/~/how-to-add-a-new-user-(local-account)
- Start Terraria with the new local profile and create a character
- Quit Terraria, switch back to the first profile, and start Terraria again
- Open your world, press '+' on the second player controller, and the second profile should display
- From there, you can select any character on the second profile and start playing!