How do I record the screen?

The normal Daydream chord to record the screen is Daydream Button + Vol Up or Home + Vol Down. On the 6DoF controllers, these have been remapped to Daydream Button + Grip (screen video record) and Daydream Button + Trigger (screenshot). For both of these, first hold the Daydream button for one second (until you see a screen flash), then press the second button while continuing to hold the first button. Hold down both buttons for at least 300 ms. You will see the screen flash white for screenshots and a red dot will appear for videos. Repeat this chord to stop recording video.

Why did the two controllers not pair properly?

See pairing.