The computer handles most of the complexity. In a player turn a player has some simple options. A Korps adjacent to an Army can Retreat, Defend, Probe or Attack. A Korps that is not adjacent to the enemy can either Hold or Deploy. Main Effort allows an enemy city to be targeted as an objective of the Armee and its Korps.
Main effort chews up supply and administration.
Normal is what it says. Normal is good for defending. Normal is also the only posture that allows the Armee HQ to be voluntarily moved to another city. Rest is good for restoring supply and admin levels. Korps in an Armee are reduced to skeleton levels - typically only two divisions.