The new User ID is separate from your Nintendo Account, but you’ll need one of those to claim your unique name that will likely serve to identify you in the company’s online universe, or something connected to Switch games.
It’s also not the same as the Nintendo Network ID you used for Wii U and 3DS online services, as well as the Miiverse and Nintendo eShop. There’s also an account nickname, for some odd reason. The company could certainly stand to consolidate some of these to simplify registration and account management.
Anyway, back to the new Nintendo User ID. You can set it up by logging into your Nintendo account, which is associated with your email address. Once you’re in there, head to the User Info and set your new User ID on that screen.
It’s likely that this will serve the same purpose for Switch players as the Network ID did for Wii U and 3DS owners. Since the IDs are unique, you’ll want to grab your handle of choice before someone else claims it.