Current I'm still grasping the system but it's basically like this.
A,B,C buttons: Weak, Medium and Strong attacks respectively.
D button: Special motion. Also reserved for Arcana moves.
There's two special moves which I think are universal:
f+C: Wall slam attack. If it connects the opponent is sent to the wall behind them immediately. It juggles as well, but if you're doing afar you need to do a Homing Cancel.
df+C: Air combo launcher. Works like GG series' ground Dust attack. If you would like to follow after that hit you will need to do a Homing Cancel.
Both moves can be held but I am not sure what its effect are after holding, it doesn't make them unblockable iirc.
Homing Cancel is basically cancelling a move (normals, specials, supers) by pressing D, and holding the button while holding a direction at the same time. So if you're doing a launcher (df+C) you will need to do something like up+D while holding D to get to the opponent. Homing Cancels take away one skill bar (you have 3), which automatically replenishes after a while.
There's also a super bar which I think you can store up to 9 of them.
As for the Arcanas themselves, I recommend visiting the website below (in Japanese) which gives you more than enough information about the special moves and everything else, including the Arcana's abilities.