Given the long timeframe that the game takes place over, as well as the focus on being a shorter and more digestible experience, war looks a little different in Solar Nations 2 than it does in games you might be familiar with.
The general idea behind warfighting in Solar Nations 2 is that "war is not about who is right, but who is left." (Bertrand Russel) In game terms, every more-or-less balanced war will become a war of attrition, where victory is obtained not only by strength of arms but by will to fight. You might notice that the currency I have discussed the most so far has been stability as opposed to money - and that is because stability is arguably more important.
When you engage the enemy in battle, every soldier you lose takes a tiny amount of stability from you, and given that stability is difficult to get more of, this means you can only sustain so many losses before you must come to the negotiating table. So maximizing enemy casualties is still important, but you will not be able to completely annihilate the enemy army simply by being stronger than them.
Advantage
To maximize the damage done to enemies, the most important thing to understand is Advantage, as it is practically the only way to increase your damage dealt without either spending more resources or becoming vulnerable to new kinds of weapons. Every point of advantage corresponds to a +1% damage multiplier to your side, after all modifiers - battle advantage is somewhat random, but there are a few important characteristics to understand.
Battles begin with a certain advantage offset, which starts at the defenders' entrenchment minus the attackers' breakthrough, minimum zero. Each month, advantage moves 3 points in the attackers' direction. What this means is that eventually the attacker will dominate the battlefield, however in order to do this they will need to suffer many losses to keep the battle going long enough to take advantage of this effect.
A defensive battle, the enemy is taking double damage because they attacked with low breakthrough units.
Strategic Weapons
Strategic weapons can be used to significantly damage enemy territories and armies, which contributes massively to war exhaustion. In general, strategic weapons are best used to soften up enemy hard points (defensive projects) in order to make attacks against them easier, and thus take better advantage of the attacking advantage boost over time. However, they can also be used to annihilate the enemy at particular points in the game.
Nuclear weapons currently dominate our worlds military theater, as they hold the potential to completely destroy the target nation, with little to no chance of counter. In the future, nuclear weapons are less dominant, but still extremely powerful. There are defensive projects which make regions less vulnerable to these kinds of attacks, but they generally come a few years after the attacks themselves, meaning there are some small windows where MAD is back on the menu, a useful opportunity if you find yourself in an unwinnable war- as you can threaten the enemy (AI or human) to back down before you unleash your nuclear arsenal.
Big bomb makes big explosion!
Those people were counterrevolutionaries anyway.
Space
Understanding space is key to warfighting in Solar Nations 2, as your country will expand and someday get too large for the world you start on. Space is split into a few different terrain types, each with advantages and disadvantages. Generally, movement in space works exactly as it does on the ground, except that all units save those specifically designed for it will be extremely vulnerable and slow. Surrounding each celestial body are a few orbits, the number of which depends on the size and number of satellites. In most cases, this will be 2, an equatorial and high orbit. Space supremacy allows fast travel around many celestial bodies, and so is a massive tactical benefit for those who have it, but achieving void supremacy is difficult, as it is such an important objective.
Of all the unit domains in the game, space is likely the most cost prohibitive, as spaceships must be both numerous and expensive if they are to accomplish their objectives. In addition, you must consider the difficulty of spaceship construction, as large celestial bodies like Earth create challenges to ferrying large amounts of cargo into orbit, necessary for construction of a void navy. Add to that the chaotic and fractured state of our homeworld, and it may not be a good idea to invest in a space fleet early in the game on Earth.
Low and High orbit favor different damage types. (Autocannons and Lasers, respectively)