I get my games from GOG, my friends from Steam. After reading some incomplete instructions online, we were able to put the pieces together yesterday and play successfully.

These were the necessary steps in our case:
1. All players ensure that port 7777 is forwarded on their router (how to)
2. Steam players must start the game's EXE directly (...\Steam\steamapps\common\The Planet Crafter\Planet Crafter.exe) from the game folder (NOT via Steam). The reason is: if you start the game via Steam, you don't have the option to host/join via IP address.
3. The host opens a game and shares their public IP address with the other players.
4. The others can join using the IP address and port 7777.

However, we have noticed the following problems:
Logically, the host must remain online to play since there is no dedicated server. Planet Crafter does not store a copy of the save game for each player. If the others want to continue playing without the original host, the save game must be shared by the host (where to find it) with the other players.

However sharing savegames brings it's own problems (switched up inventories etc.) and you have to manually edit the savegame to make it work. So I don't recommend it.