The latest version of the Google Play Games app lets you easily record gameplay too. You simply open it, select any game you want to play, and then tap the record button. The resolution choices for capturing your gameplay are 720p and 480p.
You also have the option of adding video of yourself playing and commenting, via the front-facing camera and microphone. After you're done, it's possible to edit the video, then upload it to YouTube.
Gameplay recording will be out in the US and UK first, over the coming days. More countries will get the new feature "soon after", according to Google.