The main story takes the party across each region of Trinitia exploring the dungeons of each Arma, large weapons of the gods. Inside dungeons are altars that add a new weapon to a character or power up an existing weapon. Pressing 
will bring up the map and the next objective. You can hold off on the main story and revisit previous explored areas and do quests anytime.
Tutorials will popup explaining new mechanics for the first time and you can review them in the Help screen of the main menu.
You will want to stock up on consumable items before you leave town and enter fields. You don't have to carry the maximum as you can find more in chests. If the HP of all party members reaches 0, then it is game over.
Save at shrines when you encounter them and don't forget to level up Triggers.