I assume you're running Windows. You needn't compile anything. Just grab the self-installing package.

I assume you want to be able to connect to a VNC server that's behind your router/firewall from elsewhere on the internet. You've taken care of the first problem of knowing what your IP address is. The second problem is getting the VNC client's request to be forwarded along to the PC that's running the VNC server. This requires you to configure your router/firewall. You want to forward TCP port 5900 (which is the standard port for VNC) on your router/firewall to your PC. Exactly how you do this will depend on the particular router/firewall, but it should be reasonably obvious, I would imagine.

Note that VNC authentication is not well encrypted, so anyone who can listen in on your traffic can then get in control of your PC. This may or may not be an issue, but it's something to consider. I'm sure there are sites out there that talk more in-depth about VNC security issues than I'm prepared to here.