VNC is definitely the way to go. Install a VNC server on the computer you wish to share. Install a VNC client on the computer you are connecting from. When the client connects, they can see and control whatever is on the server computer. The person sitting at the server computer can still see and control the machine as per usual.
At work, we have RealVNC servers installed on all user workstations. IT then has clients to connect to any machine in the corporation. We connect to users as needed to fix simple issues. The user controls the mouse and keyboard to show us the problem they are having, then IT controls the mouse and keyboard from the help desk, while the user watches, to fix the problem. I think this closely resembles the problem you are trying to solve.
At home, the desktop machine has an UltraVNC server installed. The laptops have clients to connect to the desktop. Makes it really easy to set up download tasks on the desktop without having to go to the computer.
Sorry, I think this falls into What kind of questions should I not ask here?, and it seems many older questions about the same have been deleted. Many others can still be found though, and might help.
– Arjan – 2012-08-12T12:50:43.773Not Windows Remote Desktop, as that (last time I checked, doesn't do that it logs the other person off). But VNC does allow it, that's normal VNC behaviour in Windows, the 2 users can share the screen. You can even have a conversation with each other in notepad! – barlop – 2012-08-12T13:35:16.853