According to an Xbox One troubleshooting page, a 2.5mm-to-3.5mm adapter cable included with the Xbox One Stereo Headset Adapter will allow you to connect to the device for chat audio, but not game audio. For that, you'll need additional cables. If your headset uses an optical audio cable, plug one end into the headset or headset receiver, and the other into the Xbox One's optical audio output port. If your headset connects using RCA, you'll need RCA audio output ports or a 3.5-mm headphone jack output on your TV. If you've got the latter, you'll also want a 3.5mm mini-to-RCA adapter cable.
The upcoming Xbox One Stereo Headset uses a single 3.5mm jack for both game audio and chat audio, so using it is a simple matter of plug and play. Mostly. Before you use either the Xbox One Stereo Headset or the Stereo Headset Adapter, you'll need to update the firmware on your Xbox One controller. And how do you do that? You connect to Xbox Live, remove the controller batteries, plug in the adapter and headset of choice, install an update, and replace the batteries.
Update: While Microsoft's support page also lists the Tritton Primer model as an incompatible headset, a Mad Catz representative told Joystiq that information is incorrect. "The TRITTON Primer should work fine via the adapter," Mad Catz PR Director Alex Verrey tweeted.