Wii U Voice Chat Isn't Simple
Unfortunately, it sounds like there will be no standard voice chat across all Wii U games. This means that some games will support voice chat though officially-licensed, third-party headsets, but whether or not you can use these headsets to chat with other people while playing will depend on the game you are playing.
Nintendo Everything received an official quote from Nintendo saying, "Wii U will have in-game chat functionality for select games, including, but not limited to, Call of Duty: Black Ops II, Assassin’s Creed III and Mass Effect 3. This feature will be supported by licensed stereo headsets that plug directly into the headphone port of the Game Pad. Licensed headsets are available from Turtle Beach and Tritton.”
What's strange is that the WiiPad has a built-in microphone, but apparently that microphone can't be used for voice chat. Another oddity is that Nintendo's Pro Controller doesn't have a microphone jack at all. This means that players who want to take advantage of voice chat while using a classic-style controller will still need to keep a WiiPad handy just so they can plug their headset into it. Oh Nintendo, you're so silly. *ruffles hair*