It's really simple. You need to add another graphics card if your current system doesn't have the capabilities to plug in two monitors.
The system should recognize two monitors when you restart, and you can either use them as one giant monitor and spread a worksheet across multiple screens, or you can do exactly what you asked, TV in one and youtube in the other. These documents should help.
http://www.microsoft.com/resources/d....mspx?mfr=true
http://support.microsoft.com/kb/307873