There are only two pieces of software necessary:
1)x11vnc: Installed on the Linux machine to use as the VNC server.
2) TightVNC: Installed on the Windows machine to use as the VNC client.
Installing the windows software is straight forward for most users. Just download the installer and double click. For many Windows users, the installation of the Linux software might not be as straight-forward.
Of course the Linux installation will depend upon your distribution. But basically all you have to do is follow these steps:
1. Open up your Add/Remove Software tool (such as Synaptic, Ubuntu Software Center, gnome-packagekit, etc)
2. Search for "x11vnc" (no quotes)
3. Select the results for installation.
4. Click Apply to install.
Now, if you are more comfortable with the command line you can install the Linux software like so:
1. Open up a terminal window.
2. Issue a command like sudo apt-get install x11vnc (this will depend upon the distribution you use).
Once all of the software is installed, you are ready to go.
The Linux side
This is really quite easy. All you need to do is start the x11vnc server. If you look at the manual page for x11vnc (issue the command man x11vnc) you will see numerous options available for the server. One of those options you might want to consider is the -forever option. If you don't add this option to the command your x11vnc server will die as soon as the client quits the session.
So the command you will want to run, from the terminal, is:
x11vnc -forever
You will notice you do not get your prompt back. Even if you add the & character, x11vnc will not return you your prompt. Because of this, you might want to consider adding a line like x11vnc -forever to the end of your /etc/rc.local file. This will ensure your x11vnc server is started at boot.
The Windows side
Now it's time to connect. You've already installed TightVNC on the Windows machine so go to the Start menu and fire up TightVNC. When you open the tool up a small window will appear that allows you to enter an address for the connection as well as open up the Options window.