It is recommended to use the 710 or 510 USB products for this.
You will need an RCA splitter, and this will only work with Standard definition video output from the Console.
The splitter will be used to split the output Video from the Console.
Connect the splitter to the outputs on the Console, and the inputs on the TV and Pinnacle Capture device. At this point Capture is the same as any other capture. Open Studio, go to the Capture/Importer tab follow the normal Capturing procedures. For help with Capturing, see this FAQ
How to use the Pinnacle Studio Importer
This has been tested successfully with Xbox 360, we expect it to work similarly with other consoles.