Well, if you're still wondering how to learn the changed UI and battle system it would a good thing to just go and do your class quests, as they help instruct you in how to play as that class, while also unlocking abilities as well (that you can't get otherwise). Another helpful thing gained through doing your class quests is they unlock the Hunting Log for each class - although you'll have no need for the exp boost, being able to go out and solo the enemies helps you get a feel for each class in combat if you have clear objectives to do.

Another thing you could try is to run around doing FATEs as a means of training - again the exp gained would be superflorous, but it's a way of getting into large scale battles while still learning how to utilize your class or Job.