How to Play
First Steps
When you launch the demo you ar presented with a screen giving a choice between starting a scenario or changing game settings.  For now choose scenarios.  (Later you can use the "Game Settings" menu to turn off hidden terrain and fog of war, see below for discription.)  At first select the 'Carthago' one, and the Romans to play.

Once you enter the game you are the blue-colored civilization, in this case the Romans.  Familiarize yourself with the Display if you haven't already.  Lock in moves using the Units Box.  The selected square on the main map is the one that's shown in the Units Box.  Moves will only be executed when the End Turn button is pushed. For now you are at war with the other guys (Carthaginians).  The other side will determine its own military manuvers, and execute them when the turn ends, during the simultaneous movement phase.  Before the bloodbath you can check out how your  Economy is doing.  The Military and Economy models are the main attractions in this demo.
Movement
Movement is Clash is simultaneous.  You never know how many of the enemy will be in any particular square, since you don't see their movement. For now enemy military units have relatively simple AI. Hidden (black) squares are exposed as movement makes their terrain known.  Exploration will be more sophisiticated later, but for now it is in traditional Civ style.  The tiles not near a city or military units are under "fog of war" and will only show general information on the square.  Squares under fog are tinted darker than normal.
Combat
Battles take place when Task Forces (TFS) from two different civilizations meet in a square. See the Units page for more information on units that compose TFs.  Combat is only resolved after the new turn button has been pushed.  Forces will fight if they are in the same square, and the odds are roughly even.  If one side is clearly outmatched it will attempt to flee.  You will get a brief report of each combat in the Information frame.  More details (Lots of them) are available in the combat.txt file.
Other Game Areas
Technology
For now Technology is static, and is only used in the economy.  There is no real Tech model or interface in Demo 6, although much of the coding is done.  Look for it in Demo 7.
Government
The Government and Social models are fairly far along in terms of coding.  It will be in either Demo 7 or 8. 
Diplomacy
There is none, look for it in Demo 7.  Its All War all the time for now.