And just to clarify a few things since you're new and you might not know.
1) apparently training games are now called "friendly" games (I just found this out today, so I think it might be pretty new?).
2) when you create a game, the first option (at least usually, possibly always) is game mode. I think it always defaults to "normal," but the drop down menu will let you change it to "friendly" (i.e. training).
3) friendly/training is NO DIFFERENT than playing the actual game, EXCEPT you don't win/lose ELO. And if the game has a single player option, it will only be accessible in friendly/training mode.
4) as Ehrine stated, you can't START a friendly/training mode game in Ark Nova without a premium membership, but you can JOIN one. (And obviously, you can't play solo mode in Ark Nova without a premium membership.)
5) some games have tutorials, which is different than training. They are player or developer created and are basically a walkthrough of part or all of the game with explanations, but they aren't "playing" the game as they usually involved forced moves to show you how the game works.
I hope that clears some things up, and welcome to BGA!