The rule behind it
The left side (as you face the net) is the attacking side for a right-hander: the forehand covers the middle, the overheads through the gap are natural, and the finisher lives there. The right side is the steady one: the first volley, the reset lob, the ball that starts the point. A left-hander almost always plays the right, because then both forehands meet in the middle, and a pair with two forehands in the middle wins the middle. Everything else is personality: the player who wants the ball in the big moments goes left; the one who is happy to build goes right.
Once you have sides, where to stand is the next question, and the chains are where you practise the decisions from each side.