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There are a few multiplayer-related topics here, but they all use language and terms I'm not familiar with. I have two PCs in my house, we have a wireless network, and I'd like to play some multiplayer Warcraft II. In layman's terms, how do I accomplish this?
So you actually have a number of choices, some are compatible some are not.

First choice: Version of the game. From what I can tell you can pick either the new launcher or the classic launcher, both of them will likely play together.

Once ingame, click on "Multi Player Game"

Now you're presented with another choice. You can choose Enhanced (Expansion) or Classic (Original). Pick one of these types, and choose the same option here on ever person that wants to play.

Now you're at the connection screen. Basically there is only one option here that will work.

Choose: "IPX Network" and click connect.

I believe at this point it might ask you for a player name, if it does enter one and click okay.

The on the machine that's going to host the game, have them click create game. Once the first person is in the game, then on the other machine(s) you should see the game name pop up on the left side. You will then be able to select that game and click on on the other computers. If the game doesn't show up almost instantly, then you may need to tab out on the host or possibly both pcs to allow the game to communicate through the Windows firewall.

The game itself is in fact using IPX, but GOG is using a wrapper that allows it to send UDP packets across your LAN. Generally this works quite well and it shouldn't require any configuration on your end. If you have multiple network adapters connected then you might run into some additional steps that would require you to actually configure the IPX wrapper, but for most people this won't be an issue.