Both "games" feature a number of scenarios, divided into basic and advanced. The advanced ones (including the long campaign scenarios) incorporate the advanced rules, while the basic ones either eschew the advanced rules altogether or only use certain ones, and are generally shorter in duration.
Above is the set-up for the 3rd scenario, "McDowell's Opportunity," which is a hypothetical scenario that has the Federals attacking the Confederates at Manassas Junction two days before they did historically.
The game provides Force markers that you can use to keep big stacks off the main map, as shown below.
Each turn there are a number of initiative phases. Both sides roll a die and the high roll wins the initiative (generally the Confederates win ties). The initiative player either takes an action or passes the initiative to the opponent. If both players pass the turn ends.
The basic actions a player can choose from are march, assault, and activate leader (you can also burn a railroad station or entrench). Marching is both moving and attacking, though you can only attack with a single unit. Assaults are the only way you can have more than unit attack at a time. Activating a leader allows you to move several units at once, or at least sequentially, and these movements can also include an attack just like a regular march. But you can't assault unless you initiate a "grand assault" with a leader activation.
The movement is random. You roll a die and that's how many movement points you get (generally the Confederates always get a bonus). These movement points are what you spend to attack when marching, and the cost of those attacks depends on what kind of attack you're launching. I won't go into the details of combat, other than to say so far it seems to give reasonably accurate results.
Below is the general Union plan. The divisions already engaged will try to march around the Confederate left, while additional Union troops to the Northeast will move up and hold the center, mainly Centreville, which is a Confederate objective, all the while trying to minimize their losses.