There are two parts to using VNC - the 'server' that is going to run on lectura and the 'client' that will run on your Microsoft Windows machine.
To set up the part on lectura (in an SSH window for example) you would enter vncserver
The first time that you do this you will be prompted to create a password (this is a separate password from your CS unix or CS Windows passwords but you can give it the same value). Additionally the first time that you run vncserver it will create a directory named .vnc into which it will put a some default files (passwd and xstartup).
A message will also appear on the lectura screen that says something like New 'lectura.cs.arizona.edu:2 (jcropper)' desktop is lectura.cs.arizona.edu:2 Make a note of this information - especially the ":2"
On your Windows machine you would need to run a VNC client such as TightVNC. When you start this client software up it should ask you for the VNC server and at this time you enter the information from above e.g. lectura.cs.arizona.edu:2 The next prompt you should get should be for your password and for that you enter the information that you put in when you ran vncserver for the first time above.
If all of this works then you should get a new window to appear on your computer that is the default settings (at this time a grey background and a terminal window in it named 'Desktop').
To close down the VNC session you would enter, on lectura: vncserver -kill :2 make sure that the number at the end matches your session.