You can select provinces and build improvements and armies in them. The economic model is pretty straight forward, but has enough flexibility that you can tinker with. In general you get income from farming. Not all regions will benefit from them. It's nice that they don't dwell too much on this, although some folks would have wanted the extra detail and micro management.
Armies are direct correspondents to their in game pieces.
Each unit on the strategic board is the same in the tactical engine. Raising armies is dependant on what buildings you have to raise those troops and a monetary cost. When opposing troops are placed in the same territory the option is presented for combat. One of the nice features is that you do not have to engage the enemy. If you are attacking and realize that you are about to engage a superior force, you can abort the attack and hope they don't come after you.