Hi Henry,

If you want to access a computer through its public IP address you have to link port 5900 on your router to local IP address of this computer. Port 5900 is default port used by RealVNC (btw I prefer UltraVNC).

Other ports, not just 5900, are also available. After starting VNC viewer enter IP address, semicolon and destination port. For example:
64.110.219.183:5901

Several LAN computers may share same public IP address. By assigning different ports to local IP addresses you may run VNC server on each computer. Just ask your sysadmin to link external ports to certain local IP addresses.

I use UltraVNC with one of my customers, already saved me tons of time and gasoline too :)