Recording a gaming console onto my computer from my TV
You will need a USB Video Capture Device to connect the game to your laptop.  

In order to also be able to view the game on the TV, you will need 2 splitters for the video and audio and an extra composite cable.

You would run the yellow and white game console outputs to the splitters and attach the splitters directly to the Video Capture device.  The red cable goes into the Video Capture device directly.  Connect the yellow and white connectors of the extra cable between the splitters and the TV.

I'm not sure how much the video and sound quality will be affected by splitting the signal, so you may need to buy a better splitter to get it to work without any loss.