GMs are people who appear in the chat box, indicated by "[GM]" before their name; these users are also usually veteran players. GMs act as both moderators and a people who can answer any of your questions. GMs take shifts to moderate the chat, so you'll encounter many different GMs as the day progresses; however, servers that are old and empty usually have no GMs available. A GM is not allowed to actively play the game on a GM account.
To become a GM you must have a lot of knowledge of the game and then apply for the position, presumably on the official Clash of Avatars forum.