Both a friend of mine and myself have a copy of this game on GOG galaxy but neither of can figure out how to do the online multiplayer together. Has anyone been able to figure it out? Thank you ahead of time for any helpful advice.

It has a simple server-client multiplayer. One player host a server, while others connect with the host's external IP address (internal IP also works on local network). Of course during online play port forwarding is required.

How do you do that? For me it greys out the option to choose a server or anything like that.

If I remember right you should able to type the IP at the same menu where you could select a server. It should be the third.one when you select multiplayer. The Steam version at least features it like that, but you have to run the game without Steam (directly from the folder). If you use Galaxy you may have to close that program till you play.