Cortana won't be available on the Xbox One officially until next year, but testers of the new Xbox dashboard beta are starting to get early access. It's not an official roll out, but some Xbox One owners have discovered that you can enable Cortana by accessing the settings panel and going up and hitting the A button a few times.
This activates Cortana and it's immediately snapped at the side of a game or app. As the Xbox One preview is now running Windows 10, the Cortana experience looks identical. Cortana floats at the top left, allowing you to say "Hey Cortana" to enable voice commands. Microsoft is planning to support features like inviting friends to parties using Cortana, but right now it's fairly basic functionality. As the Xbox One version of Cortana is identical to Windows 10, you do get access to your calendar appointments, news, stocks information, and everything else you track in Cortana.
Microsoft is expected to officially enable access to Cortana in the Xbox One preview before the end of the year.