To use it, players simply need to sign up for a Twitch.tv account and then access the feature from the social menu in the game. Streams can be set to private if the user only desires a select few to view his or her victories.
The devs say that this move will definitely help out aspiring streamers: "By integrating an SDK created by Twitch.tv into EVE, you can now completely bypass the 3rd party software and stream directly from the EVE client. Amazing!"
[Thanks to Chrysillis for the tip!]