Player turns have 2 phases the main phase and the troop placement phase. In a really odd design choice the main phase comes before troop placement, so you can't do anything on your first main phase. In the troop placement phase you can only deploy units on specific parts of the map, which you may have to actively look for cause the camera doesn't always start on that specific area of the map. You will have 15 turns to find and destroy all enemy units. Once you click on a unit the panel on the left of the screen will give you its information including how much ammo and fuel/energy it has left which is very important. I suggest making heavy use of aircraft especially the light bombers because most early enemy units can't fight back against them. I also recommend you always have a couple of regular infantry and trucks to move them across the map so you can take over the bases that the enemy will inevitably hide units in in the later turns once its decided it can't win. I should also mention that at least on the maps in china after you have killed several units the enemy AI will focus entirely on hiding a couple of units just to keep you from winning. I hope this has been helpful.
Edit: Also at least on the maps in China you will want to send in as many officers and units as possible or you probably won't have the fire power to get the job done.