Offensive Advice -- Finally!
Given the feedback I've received, I should probably make the title larger and italicize it. However, this article may not cover the 'tactics' everyone is interested in, but again, we must start with the basics.
Know the Units
Knowing the individual units is critical to any form of offense and defense. In some games, there is little to no difference. For example, in the game 'Here I Stand', all units are effectively the same based on type. All Naval Units have the same value, all ground units have the same characteristics. Only the Ottomans have any different 'types' of units with their Cavalry and Pirate ships. This does reflect the organizational units of the time.
For most games, units exhibit significant differences. Regardless of era, these can usually be categorized in the following way:
Infantry - Infantry form the basic unit of every army. Infantry perform nearly every task equally well, except for naval actions. Infantry can hold a position defensively, and are expected to assault enemy positions with equal vigor. Normally, the basic infantry are better at defending a position than attacking a position and so in infantry 'Quantity beats quality' tends to exist.
Armor - Armor units represent units with heavier armament and usually take more effort to bring down. In modern usage, armored units consist of tanks, self propelled anti-tank guns, and armored personnel carriers. However, I would argue armor has always existed. In ancient times Chariots could be considered armor. During medieval times, Heavy Knights would constitute as armored units. When looking at ancient Greek city-states, the Greek Heavy Infantry (Phalanx) could be considered armored units.
Armor units usually do well in offense and not so well on defense. Usually armored units must travel in larger groups for safety, and so they don't do well where terrain would force the units to space out too much. Forests, Mountains, and Broken Terrain are anti-thesis to armored units.
Cavalry - Cavalry units perform the role of recon, scout, and follow up after an attack. Cavalry rarely engages in fights until the battle is over, or nearly over. Cavalry units tend to move fast and perform 'hit and run' tactics. Left on their own, cavalry forces will fall to any other unit quickly if it is a sustained operation. This makes cavalry effective as an attacking force, but not in a 'head-to-head' way. Cavalry should strike behind enemy lines, at the baggage train or supply lines of the enemy. They move faster than other units and should strike quickly. Cavalry can operate over most terrain types effectively.
A common misconception is 'units on horses = calvary unit'. Heavy Knights often lack the long term speed and endurance necessary for cavalry. They may execute a 'cavalry charge', but that does not make them cavalry.
Sappers/Engineers - Sappers, or Engineers, perform very specialized roles. Their combat ability is often rudimentary, if not worse, than common units. However, they make up for it by having better fortifications or being able to assault fortified positions. In game terms, these units often have superior attack and defense values than other units in the game. Sappers require extensive training and specialized equipment to perform their job. Sappers/Engineers usually fortify a position, or prepare the assault on a position, and then other units perform the defense/assault. In proper use, Sappers/Engineers will be committed to a battle only after all other units have failed and success hinges on sheer numbers.
Skirmisher Units - Skirmishers, at their most basic, are slower moving cavalry. They move quicker than the main body of infantry, but are not as strong in either attack or defense as other units. Skirmishers operate best in difficult terrain and over longer distances. Skirmishers don't 'hold the line' but 'extend the line'. A common use for Skirmishing units is to fill in the defensive gaps of the main units. However, this is not how they are designed to be used. Skirmishers should harass the enemy from the sides, provide flanking attack bonuses for other units, or exploit a newly created hole and attack unguarded artillery.
Archers/Snipers (Ranged) - Archer units are units with exceptional attack range which are not armored. Archer units are often weak up front, but their power is to support the main units, bringing fire to bear from a distance. In the case of modern warfare, where every unit carries guns, the Archer can be considered 'snipers'. Snipers typically can shoot from much further away than their rifle armed comrades, and with great accuracy. There is a fine line between Archers and Artillery units, usually depending on the era. In Ancient times, bowman may be considered as Artillery, whereas in medieval times bowman would be Archers and canon fill the role of artillery
Artillery - Artillery units are another unit I would argue have always existed. The primary duty of Artillery is to fire from a distance on enemy units. Later uses for Artillery include the ability to assault, or soften, fortifications.
Traditionally, artillery units affect large areas of space over a long distances, and are weak, or useless, in a close fight. In some ways, ancient bowman fit this bill as they were used to rain down arrows over an area from a distance. English Longbowman could be considered an artillery unit of its time, although they also performed the Sniper role.
Siege - Siege units perform the roles necessary to assault enemy fortifications. Many other types of units may perform the siege role, including artillery and sappers. Regardless, siege units are required for the taking of fortified objectives. Catapults, Trebuchets, explosive barrels, and towers are all forms of siege weapons. Siege units need extra protection from attack. Even Sappers, which may be a good fighting force normally, usually require extra protection when they constructing tunnels (sapping) under the enemy walls.
Naval - Naval units move on, or under, the water. That seems pretty basic, but usually naval units are critical to a war plan either as fire support or to protect the supply lines. Naval units come in many types, but often they perform the same role as an equivalent ground unit (ex: Battleships = artillery, destroyers = Cavalry, etc.)
Air - Air units move through the air. Like naval units, they may perform other roles (helicopters = cavalry, bombers = artillery/siege, etc.). There are two major distinctions with Air units, however. First, Air units normally require a base to which they must return, whereas naval units can remain at sea for extended periods of time. Secondly, Air units are very responsive and have an incredible reach. Terrain does not affect movement of Air units, although weather might. However, Weather affects ground, sea, and air units.
Submarines form an interesting blend of naval and sea units. Submarines travel beneath the waves, much as aircraft travel above them. Submarines can remain at sea for extended periods of time, unlike aircraft. Submarines perform the duty of skirmishers and sniper. Unlike other units, submarines rely on stealth and the ability to slink away unseen. They are the only unit which may be completely bypassed without incident, moving unseen to strike without warning.