I connect to my windows vista machine that runs TightVNC server. I want to set things up so that, the person who connects via VNC can use a separate desktop and another person can work on the machine parallelly without interference. How to do this?
TightVNC doesn't provide this feature. Microsoft's Remote Desktop can do this in conjunction with Windows Terminal Services, but for that you'll need to purchase licenses.
Alternatively, you could install another instance of Windows Vista in VirtualBox and set up TightVNC in there, but you'll need to purchase a separate Windows license for this instance too.
VirtualBox (free and open source)