easy cap

Potato cam works fine as long as you can tell what's being played. Av capture cards run anywhere from 7-40ish, so there's a wide range of options. Basics for recording: Capture card that's AV compatible Splitters to put it to your tv and to the capture card.

You could also do something like show your phone screen on your computer, point the phone camera at your game and just leave it there for a webcam recording.