The easiest way would be to set up your mom's router to port forward (NAT) TCP port 5900 to whatever her internal IP address is. Then you open a VNC connection to her external IP address and it should connect.
A slightly more advanced setup, and way more secure, would be to to turn on a SSH server at home (simple if she were using a Mac, unfortunatly with windows it's additional software) and NAT port 22. Login with ssh and forward local port 5901 to her internal address and port 5900. The ssh command would be:
Code:
ssh -L 5901:her.internal.ip.address:5900 username@her.external.ip.address
Then connect your VNC client to "screen 1" (aka, port 5901) to "localhost" and it should tunnel over SSH securely.
Yet another method using VNC is to issue a reverse connection, which would be useful if you have access to your router but she does not - However, it sounds like since you're on a school's network and she probably has a cable/DSL connection, she has more flexibility than you. I'll save how to do a reverse VNC connection unless you find you need it.
The final method with VNC is to use an intermediary host to pass data to, e.g. a webhost account like dreamhost that has ssh access. It would require that both computers have SSH clients, which is built in to OS X, and a simple download of PuTTY for Windows. In this method, she connects to the remote host and forwards a
remote port to her internal address and port 5900, you can then forward a
local port from your machine when you connect and connect VNC again to localhost. I personally use this all the time to get past an aggressive firewall at work.
There are probably lots of other screen sharing apps out there with simple setup, but VNC is a great tool. Combined with SSH it becomes damn secure, and you can do things like password-less logins with public/private key; Essentially you can make a script that your mom can double-click when she needs your help.
