Fighting Wars discusses what affects combat, preparing for war, managing units, and finally the effects of occupying enemy terrain. You should be familiar with concepts from the earlier article Game Mechanics.
Units always consume supplies which they carry with them. In well-supplied, friendly territory, units will receive enough supplies from regional stocks that running out will not be an issue for all but the most demanding units (anti-aircraft, tech-enhanced artillery). However, in poor friendly terrain or enemy terrain units can exhaust their supplies. This is indicated by a yellow (low), then red (empty) HUD icon for the unit. When units are out of ammunition, they cannot fire; when they are out of fuel, they cannot move. Many motorized units run out of fuel before ammuniton, so while they may have a red HUD icon, they are often not defenceless.
Newly-captured land does not provide supply until you have held it for one day. Thereafter, its supply strength increases daily. To supply units in hexes 'out of supply' (0% supply), supply trucks, helicopters, and transport aircraft can be used. Simply move a stocked transport within the target unit's zone of control (one hex around), and it will automatically distribute supplies. The transport will eventually exhaust its cargo, so let it sit in a supplied hex to restock.
Military initiative is a setting which lets you specify how much independence the military AI should have. It is found under the first panel of Operations, at the bottom. At 100, the default, the AI will act as if a general, controlling everything it knows how to, in the same way the AI regions around you manage their military. At 0, you have full control of your military, and, with rare exceptions, units will not do anything unless ordered to by you. Between 100 and 0 there are levels at which they AI will do some things (e.g., send units to base for repairs) but not others. However, these levels aren't stated anywhere.
Units' experience can have a great effect on their combat power and susceptability to damage. Having experience at 100 should make a unit about twice as effective as its base values. This advantage is diminishing, however, so there is not the same increase for having a unit with 200 experience.
Close combat attack and defend values are used when one unit involved is in a close combat/low visibility hex. These are cities, many bases, dense forest terrain, and so on. If two units are both in close combat hexes, then all the attack/defense values used are those of close combat. If one unit is in a close combat hex and its opponent is not, then the first unit would defend with close combat values (it is in close combat terrain), and attack with normal values (its target is in normal terrain). Likewise, the opposing unit would attack with close combat values (its target is in close combat terrain), while it would defend with normal values (it is in normal terrain).
The close combat, supply, and defensive strength overlays show factors affecting combat. Note their appearance below.
Bases produce military units, and serve as sources of supply. Each base can produce a specific number of units at one time (except airstrips and sea piers, which produce none), and are identical in how quickly they repair damaged units. Larger military bases produce more units, are more efficient in the number of personnel required per build slot, and produce much greater supply at further distances.
DEFCON (Operations) sets the alertness level of your military. Higher levels bring greater unit efficiency, production rates, and efficiency, but cost significantly more with each level. DEFCON's effects on efficiency take a few weeks to implement, and a rise in DEFCON from an AI region may be taken as a sign it is preparing for war. Be aware also that units which are in reserve have their efficiency gradually lowered. When deployed, they require a few weeks to achieve their full combat power. This applies also to repaird units. Units which have just finished production, however, will deploy at the maximum efficiency of your DEFCON and spending.
Reserve personnel are used to staff all bases and units, and a shortage of these can cause bases to remain inactive or units to be unable to deploy. More can be recruited by raising military salaries, introducing conscription, introducing coed combat, and finally by lowering the conscription age. For quicker relief, unused bases can be deactivated to free up tens of thousands of personnel. Deactivating air strips and sea piers has the least negative side effects. Beware the supply effects of deactivating a military base, and remember sea terrain cannot be in-supply without at least one active sea pier or sea base.
Salaries and maintenance spending, under the Defense tab, have a direct influence on your rate of recruitment and military efficiency. Raising funding above recommended will further raise efficiency, but at diminishing returns.
Missile production is tied to the number of regional airbases. Each airbase allows the simultaneous production of six missiles. These missiles can be assigned by pressing <M>. Producing anti-ship missiles will probably be your most significant concern, as they are essential to naval warfare.
War is declared by clicking a region's name under State, then clicking the last button "Declare War". You must have sufficient casus belli (State) to avoid giving all other regions reason to attack you, and lowering your standing with the World Market. If you have chosen to invade a region, it will probably have a lower DEFCON than yourself. This gives your region an initial efficiency advantage. However, if the opposing region has a high World Market rating, and you have a low rating, then it may receive World Market military advisors, which can significantly boost its efficiency. To avoid this and more serious sanctions and expulsion by the World Market resulting from your military action, it is often best to wait until a region declares war on you. This becomes especially important in the harder difficulty levels, where regions and the World market are predisposed to hate you.
Repairing units can greatly help maintain combat power. Ground units which take over a month to produce can be repaired from a badly damaged shell to a full-strength unit in a week or less. Pull damaged units back, then asign them a "repair" order on a base, and they will repair most quickly. However, they will come out of reserve at efficiency similar to that of a reserve unit (low). These units can also be left on terrain to repair. While this is slower, they do not suffer the reserve efficiency penalty. Note that the higher the supply of a hex, the faster a unit will repair on it.
You will probably benefit from organizing your units when the scenario starts, to form stronger combat and stand-off stacks. Units such as infantry, tanks, and anti-tank are normal units which can stand toe-to-toe with the enemy. These can easily be organized together, though some units are more suited to different terrain (discussed later). However, artillery and anti-aircraft units are stand-off units. This means they are not intended to be in a hex right next to an enemy unit, where they may be attacked (and destroyed very easily). These units are most safely separated, and placed behind front-line units.
Large numbers of units can be particularly difficult to organize. Using the "Add All Units Of Same Type" and "Add All Units Of Same Class" buttons which appear when selecting units, one can quickly select most units. Clicking either button once will bring up all units without orders, while clicking either button twice will bring up all units, including those entrenched. To reorganize your forces, select all units of a type, and order them to a single hex. The units will reach the hex, then expand out in seven-hex stacks due to the stack limit. In this way, one forms their units into maximum-strength stacks.
Large numbers of aircraft can be accommodated by building airstrips in a circle around a principal airbase. Units which cannot land at the center airbase will land at the outlying ones, thus preventing them from losing fuel and efficiency.
Missiles are most effective in extremely large numbers. Many units, particularly ships, are adept at destroying missiles. However, their rate of fire is limited. Therefore, the most missiles will strike their targets when fired overwhelmingly.
Ground units can be transported via transports from all three branches. Select the unit, then right-click its destination and click "Air transport" or "Sea transport". If the unit can be transported via helicopter, it will sit while a helicopter picks it up. If not, it will move to the nearest airstrip. "Sea transport" will likewise cause the unit to move to the nearest sea pier. If the unit's weight is too much for any transport, it obviously cannot work, but you will not receive a notification, so check the weights yourself.
Transporting units in this way is fast and easy, but can be wasteful. Especially with sea transport, transports which can hold many units may take only one of many waiting units and leave for the destination. To better use your transports, move the transport and units to the hex you wish to load at, then select the units and go to advanced orders (right-click, last option). Select the option "Load into", then the transport. Now select the transport, right-click on its destination, and click "Unload". This is the only way to move units via land transport. When using transports, note that the cargo of transport units which take damage will receive damage as well.
Terrain which you have taken from its owner behaves differently than your own. Because its people are loyal to the original government, and not yourself, production will be about 67% of its maximum. Further, industries, upgrades, and bridges in enemy territory cannot be given a "Destroy" (gone the next day) order without the presence of a destroy-capable unit (e.g., engineers, tanks). However, supply will be at the same levels it would in terrain loyal to you.
Bases and research centers which are captured lose 10% of their strength, and require time to rebuild. Bridges which are damaged and then taken by a region will become unusable, pending reconstruction.
In the long-term, captured territory's retarded production can hurt your region's efficiency. You may find that the enemy region has shortages in commodities, which you must now fill. (Electricity shortages are common, because few regions have excess capacity, and production is lowered for all captured plants.) Conversely, this region may have excessive or extremely inefficient industries, which your unemployment or cost-per-unit figures may benefit from by shutting these down.