In this war game you send your soldiers to barracks and other buildings on the airfield, to conquer the entire airfield. You can do this both from the ground (from the barracks you conquered) and from the air (from the 'airport units'): in that case you drop paratroopers. Your enemy has the same goal, so send your soldiers to the right strategic places and don't let the enemy conquer your buildings! Above the buildings you can see the number of soldiers you can send out.
Hold the left mouse button while drawing a line between one building and the other (you want to conquer).