Game Mechanics the beginner should be aware of are detailed below.
Hexes make up the game map. Their size varies with each scenario, anywhere from 7 to 35km+ per hex. The range of units thus varies with the size of the hexes. On small maps, the upgrades (industries, bases, farms, and so on) you see on the map are 'small', and can only be placed every-other hex. Larger maps have 'large' upgrades, and these can be placed next to each other. Hexes have different terrain types, which you can see by pressing SHIFT-F5. This view mode can be useful when planning military movements, as the player can clearly see rivers, mountains, and so on (which all have their own movement penalties, and defensive values).
Terrain Information (<F2>) allows the player to see detailed terrain information and measure distances. Movement penalties are shown, with a fuller bar meaning less impediment. To measure distances, select View Hex Resources and move the mouse to a neighboring hex. You will see the distance displayed on the bottom of the panel. Loyalty values are displayed under Terrain Information for every hex, but they are essentially unimplemented. You will receive decreased production (-33%) from hexes unloyal to you, but these hexes will neither change loyalty towards you nor rebel.
Supply is also shown under Terrain Information, as a bar. This is useful in areas with consistently high supply. Otherwise, the player can press <S> to see the supply overlay for all hexes. Supply is a critical value which determines how many resources reach industries and units. Industries produce more in greater supply, construction takes place faster in greater supply, and units recover supplies faster in greater supply. It is generated by military bases and cities, and its effects amplified by highways and railroads (and retarded by mountains, rivers, etc.). Players may wish to make the most use of their infrastructure by locking Infrastructure (Interior Dept.) spending at 100%.
Every map has a stack limit of 7 units. Only 7 units can be placed in a hex before the AI tries to move some of them away (regardless of AI initiative), and penalties are incurred during combat for being overstacked. Units in a superstacked hex will essentially fight with the strength of 7 units, when penalties are considered.
Units' zone of control extends one hex around them in every direction. Within this zone of control (ZOC), units can engage targets (even if their range is less than the distance to the next hex). If you give Engineer units a Construction order to speed up facility construction, they have a positive influence throughout their zone of control. Likewise, a supply truck (or cargo aircraft or ship) will distribute its supplies to units within its zone of control.
Be aware of the special rules for engaging stand-off units, such as artillery and anti-aircraft. If a stand-off unit is in a hex alone, a ground unit can attack it like any other unit. But, when a regular ground unit (infantry, tanks, etc.) is in the hex as well, the stand-off unit cannot be attacked until the ground unit is finished. This can be used to protect artillery and anti-aircraft, and let them escape. Note that indirect fire or aerial/naval attack has no such need to attack the ground unit first.
Spotting and stealth strengths are unit attributes which determine whether units are visible. Units with higher spotting strengths will see higher stealth units, with their most effective spotting being done close, and then fading away to their maximum spotting range (though apparently not linearly). Similarly, higher stealth units will be able to be invisible to more units. High stealth ratings are around 100-130. When a unit is moving or firing, its stealth rating is halved (double if doing both).