My brother and I bought Battlelore recently, and are ready to play the "tutorial" scenario tonight. The only thing we want to be sure about is the left/center/right positions of the battlefield. In the rulebook, it states that the left and right sections of the battlefield are subjective to the player ordering the units. So if my brother and I are sitting across from each other, my "battlefield left" will always be his "battlefield right", correct?

Yes. This is a nuance rather important to remember when resolving cards such as Counter attack .

Enjoy the game!