Gloomhaven's online mode works using a host system. To start a multiplayer game, start by launching the save of your choice. Once on the map, click on "escape" and choose "Multiplayer" mode. You are now the host for this game!
You will see that a code has been generated. Communicate it to your friends, so that they can join your team from the main menu by clicking on "Join session". You can also directly invite your Steam friends once Multiplayer mode is activated.