The Wii U firmware update that just went live and will be mandatory for any of the system's online features has enabled me to start adding friends to my system.
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The system is pretty easy. You press the Home menu on the GamePad controller, tap the Friends List option, and then start typing in the names of friends. You don't type in their real name. You type in their Nintendo Network name. They then have to type in yours at some point. After that... voila! You're friends in the system.
You can have up to 100 friends and can block people. I'm sure there's more you can do, but this thing just went live. Still exploring...