The A3! mini manga series is a commentary manga that gives you a quick understanding of the charms and basics of how to play the game, as well as short interactions between a couple of characters in each of its 4-7 panel chapters. The story is updated every Wednesday (JST).
The manga can be read officially on the official site. As for now, there is no current official English translation posted on a website, however, you can keep up with the comic by reading the English translated version by the English A3! Twitter account.