Someone I know was told by their internet provider they have an open port or proxy. They were basically told they have to fix it themselves or they will be charged for a service visit or have their internet disconnected.

How WOULD this be RESOLVED? What would the steps be?

Thanks Is your friend heavy downloader (torrents, P2P)? Did he/she play with port forwarding?I'm not sure truthfully. I know she works with computers.

I know that an open port could be USED to make a zombie computer, but that's as far as my knowledge goes.

Port forwarding?Some people tweak their routers, by opening some ports in order to achieve better download speed, thus breaking download speed cap established by their ISP.
I've read about cases, where ISPs complained about it, that's why I asked, if your friend is heavy downloader.An open proxy could be an indication that the computer is infected with a TROJAN. Nefarious persons could direct their internet activity through such a proxy in order to avoid having their real IP showing up on any LOGS. Maybe you should take the computer in question through the steps listed here?