Download the .bat files: Dropbox.com Place them in the same folder as GZDoom and the Hunter's Moon files, otherwise they won't work properly.
There are Client and Host files, in this step it is recommended that the person with the strongest computer and internet connection becomes the host.
If you are hosting the match for more than 2 people, then you have to edit the Host bat file and change the last parameter "-host" to the number of people whos going to join, this includes your own computer (so like when it's 2 people playing the default is -host 2 because it is 2 machines in the match. 3 people? -host 3. 4 people? -host 4, and goes on).
The host needs to give its direct IP to the connecting players, you can easily know the IP by visiting sites like: Showmyip.com the number shown there is what the clients will need to connect.
The client players then will need to edit the client bat file last paremeter "-join" to the IP provided by the host.
After Host and Client properly edited and saved the files, double click them and everyone are ready to go and hopefully GZDoom should start normally with a brief change in the loading interface, where it shows the number of clients connected to the match until it is completely filled, with everyone connected, GZDoom will proceed to start the game.
Mind that the limit of players imposed by GZDoom is 8, this is hardcoded and can't be bypassed, if more people want to play, another person will have to host a second match, and the remaining people should connect to that one.
Everyone MUST be using the same versions of the files and the same version of GZDoom, using different content will result in eventual "Out of Sync" message in your screen during gameplay which means what you are experiencing right now in your game is not the same for the other players and vice-versa (i.e different places, shooting against walls, walking against walls).
If everyone has followed all the steps just fine but GZDoom is stuck in a black screen forever or frozen in the very first frame of the spawning animation, someone is having problems with the modem/ISP and will have to further dig into this topic in order to discover what's up with it: Forum.zdoom.org
If the game is becoming too "jittery" or unresponsible, this is probably someone's computer not being able to keep up with the mod's demand of hardware, GZDoom multiplayer works by fully and strictly synchronizing all the machines connected, if one of them is failing at processing everything and going low on framerate, everyone else will experience that in form of stuttering movement/input due to having to wait for such machine to resume the processing.