Here's a little run down.
Enemies will aggro towards the person dealing the most damage, so if you continuously use arts as Shulk, enemies will gravitate towards him (which is bad). Characters like Reyn and
can aggro the enemy towards them so squishy characters can take a step back. You can tell if the enemy is aggro towards you if you have a red ring around your character.
You have a party gauge in the upper left hand corner. That increases every time you use an ability correctly (ie using back slash on an enemy's back), press the button prompt correctly, or defeat an enemy. You can use one bar to revive people by standing next to them and pressing B.
Each character has a talent art that can only be used when they do an auto attack a certain number of times. This is the Art in the middle of the row of abilities.
There's a system of Break>Topple>Daze, where each ailment can only be applied if the previous is (as in you can usually only topple an enemy that has break). Break does nothing while Topple immobilizes the enemy and Daze completely stops the enemy. I think at this point of the game, Shulk can break, and Reyn can topple.
Important! Non Monado characters cannot hurt Mechon enemies without having them be toppled first or using Monado Enchant!
Hopefully this will help as a primer.