This functionality integrates on the Call of Duty Elite side as well, with streams and links to the streaming user's player card accessible directly from the portal. All you'll need to get started is a YouTube account, though you'll also need a Call of Duty Elite account to take advantage of the enhanced features there. The press release also notes that additional "live stream destinations" will be announced at a later date.
It's not clear if the livestream support in Elite applies to the mobile apps or if it's just in PC/Mac web browsers. It's also not clear if livestreaming applies only to multiplayer or if you can expect to see campaign or Zombies livestreams as well. We're checking in with Activision and will update this post accordingly when we hear back.