Artes are the attacks your characters use during battles. There are three different kinds of Artes; Assault Artes (A-Artes), Burst Artes (B-Artes) and Mystic Artes. Every single Arte uses a preset amount of CC, so make sure to manage your CC gauge to make the best of your combos. You can have up to four B-Artes assigned to a controlled character, and you have the option to turn off most Artes for AI controlled characters. Characters only start with a select few Artes; the rest have to be learned through Titles.
A-Artes are your basic attacks and are split into a tree formation; they are basically tiered in nature. Every character starts with a 1CC A-Arte and it branches from there; 2CC, 3CC and then a final 4CC (a total of 10CC for a full chain of 4 A-Artes) one. You choose different A-Artes by holding the left analog stick in a direction and pressing the X button after the 1CC Arte.
B-Artes are your specials, and there are both attacks and recovery ones. Like said before, you can assign up to four B-Artes for a character you control, with the same premise of holding the left analog stick in a direction and pressing the Circle button. There are two kinds of B-Artes; instant attacks and spells. Only Asbel, Sophie and Hubert have access to instant B-Artes, while pretty much everyone (except Asbel) have spells which must charge first before they are cast. There is a way to increase the charge time for spells, which is to cast it while in the middle of an A-Arte combo; if you cast a spell just standing there, it can be slow, but if you cast it after using a 3CC A-Arte combo, then it will charge faster.
Mystic Artes are sort of like ultimate attacks, in that, you can only perform them at special times. Once you have learned them through Titles, your eleth gauge must be full and you must be in an Eleth Burst. During a combo within an Eleth Burst, hold down the L1 button to use a Mystic Arte. There are three levels of Mystic Artes (4, technically, with a Title you learn during the Future Arc) that can be learned and your Eleth Gauge can be filled 3 full times by performing actions in battle. At level 3, you can pull off a Level 1 Mystic Arte 3 times, or a Level 3 Mystic Arte once.