How to connect to a VNC session through a tunnel using putty
Create a session profile
Use the IP address of the remote computer you are connecting to. The ssh port is 22 by default.
Enable compression to make the session faster
Setup the tunnel options
The default VNC port on Mac is 5900. On linux is often 5900 or 5901. The source port is a free and open port on your local machine. (You may need to open that port on your firewall). The 'local' radio button should be selected. Click add, go back to sessions and save the session for next time. Then login to the remote SSH server as you normal would with your userid and password:
Launch vncviewer
Using a vnc client such as TightVNC, select locahost:50005 (or whatever local port you use):
You will need the VNC server password, naturally. You'll need to ask someone who knows what it is!
Getting the VNC Viewer to Set Up the Tunnel
Many of the vncviewer programs know how to set up an ssh tunnel automatically. You can use the -via option to enable this from the command line:
vncviewer -via username@142.204.133.122 localhost:0
This instructs vncviewer to set up an ssh tunnel to the account username on the specified host, and then to connect the VNC server for display 0 on localhost (from the point of view of the far end of the connection, i.e., 142.204.133.122 in this case).
In order for this to work successfully, ssh must be installed on the same system as vncviewer, and it should be called "ssh" (as exists in OSX and Linux systems, and in mozilla-build on Windows). If you're using putty, copy or rename it to ssh.exe, or use the VNC_VIA_CMD environment variable to specify the ssh command name (see the vncviewer documentation for details).