What equipment is required to record game play and commentary and post to YouTube?
Assuming that you're looking for a low cost option, the key words you need to Google are "HDMI HD GAME Capture" which will result in hardware like this HD 1080P Video Capture HDMI Recorder with SD Card Slot for XBox 360 One PS3 PS4


The HDMI pass-through function guarantees smooth HD gaming
experience even while recording.
Record 1080P HD video into USB    disk or SD card directly, no PC required.
Supports all video sources input: HDMI, component, composite.
Pass through 1080P HDMI to display on big screen.
Record your voice with video together through microphone input.


£55 + shipping...bargain - and doesn't hog your PC whilst recording.

That should be all you need but, if further editing is required, google some free video editors to try out or you can perform basic trim and edits on YouTube...here's how.