I used to have a Partnered YouTube Channel, Where I would commentate and capture Call Of Duty gameplay.
The hardware I used was a HD PVR from Hauppage. http://www.play.com/PC/PCs/4-/7791395/-/Product.html
They retail at around £120.00
How they work:
Your console (ps3/Xbox) connects to the PVR (IN channel ) Then the PVR has a "out channel" Which connects to your TV,
Then there is a USB, that connects the HD pvr to your pc,
Yes, The PVR will also do audio, and no extra cables are required for this.
Install the software that comes free with the Hauppage PVR, and your good to go,
Id recommend making sure you have a graphics card with at least 256mb ram.
Hope this helps.