You don't. A VPN is a Virtual Private Network that you use for things such as proxying your own network traffic through, or providing a secure connection to a private network over the Internet. There's no way this can keep a server online while your home computer isn't up.
You may be thinking of a VPS (Virtual Private Server), which is basically a virtual machine on a server that acts as your virtual dedicated server in that you have root access but you aren't the only one on the overall hardware. It's not always exactly a VM, but that's just the general idea of it. Since AC servers have very low local resource overhead, a VPS is a common choice for hosting them.
http://en.wikipedia.org/wiki/Virtual_private_server
It's not going to happen for free, I'm afraid.
You may be thinking of a VPS (Virtual Private Server), which is basically a virtual machine on a server that acts as your virtual dedicated server in that you have root access but you aren't the only one on the overall hardware. It's not always exactly a VM, but that's just the general idea of it. Since AC servers have very low local resource overhead, a VPS is a common choice for hosting them.
http://en.wikipedia.org/wiki/Virtual_private_server
It's not going to happen for free, I'm afraid.