I need to learn how to VNC ...

You need a VNC Server to run on the computer you plan to access. Some OSes like Mac OS X have a VNC Server built-in (just turn on screen sharing and enable VNC access). If yours doesn't you can use a free one like tightVNC.

Then you need a VNC client of course to access it.

To access through a router, you normally have to port forward. That is you have to point the VNC connection's port manually to the computer you want to control. VNC's default port is 5900. Every router has a different way to setup port forwarding. You can find just about any tutorial for any router here: portforward.com

If you want to VNC over the internet so you can access your computer anywhere without the need for 3rd party services (like Apple's back to my Mac or logmein), you can easily do this with a dynamic DNS. That is you get a static name like "yourcomputer.com" that syncs with your dynamically changing internet IP (Most ISPs charge more to allow you a static IP). I use dyndns.com, which is completely free. You'll get one like "mycomputer.dyndns.net". Then you simply download a small utility, located here, to your computer you want to access via VNC, and this utility app will run in the background making sure your dynamic DNS name is linked to your current IP address.

Some ISP's / internet routers have issues with allowing you to use the Internet IP address of the ISP to access your computer locally... so it's best to only use the DNS name when you're away from you local network, but when you are connected to the local one, just use the normal local IP.