Preliminary Thoughts:

There is an awful lot going on in this game
Do the tutorials and learn to locate and flip to different menus
Learn the utility of each of the displays
Learn what all those symbols mean

The tutorials give you the basics for getting around the game. If you haven't leafed through the manual some things that happen won't make sense.

I have been playing at “gods-eye view”. Immediate orders rarely are; order execution is dependent on commanders and sub-commanders – these guys have ratings (charisma and initiative) that influence how well/fast they get things done. So do not be surprised if orders issued to different corps are enacted at different times.

Make sure you issue the right order for the job you want done.

The manual implies that drawing the line beyond the enemy position will make the line attempt to take the enemy position (I imagine in order to reach its actual goal) I have seen this work, and I have seen it lead to a lot of units standing around “concentrating” forever. So far, it seems the most reliable method is to use the “Attack Unit” command if you want something done.

Artillery.

Still figuring out how all the commands work exactly. “Fire on Zone” works nicely as an area denial mechanism; again “Attack Unit” seems most effective in laying the smack down on a specific enemy;
“Barrage” is something I'm still playing with.

This barely scratches the surface.
The AI has been slagged for being passive/incompetent. In the tutorial it definitely is; more a strawman for practicing how the basics work.

In my first battle outside the tutorial I faced a huge Russian army. I deployed my corps in a defensive line and let the game run. The AI took the initiative (after a while) and attacked. It eventually swept my units from the map. So the AI can do things and is not inert. It would have been different with a more active player – certainly longer. Whether the AI is up to holding off a player in a more dynamic battle remains to be seen. I suspect it will have trouble keeping up with constant change and shifting tactics...but we'll see :)