War and Combat
Land Combat
You will have to fight in this game, no matter how peaceful you may wish to be. Early on, the Barbarians will come after you, and they cannot be reasoned with. And then you may attract the greedy attention of other Empires who want what you have. So you have to be ready, and that means you have to build military units and learn how to use them effectively. There are 3 types of military units available in this game: Land, Sea, and Air. And they take the stage in that order. When you start out, you have a Settler unit that can found your first city, and a Warrior unit. I will generally use my Warrior unit to explore for the first 20 or so turns because experience tells me that is safe. And while I am doing that, I will build at least one, and often two, Scout units to take over the exploration.
And by turn 30 I have probably discovered a few Barbarian Encampments. Taking them out is a good idea, because clearing them can yield a bit of cash. As long as Encampments are left alone, they will turn out Barbarian units that will harass you and anyone else in the area. If an Encampment is near to a City-State, you can earn some increased status with the City-State by clearing it out. A Warrior unit is the earliest military unit available, so it is not particularly strong. You might want to be careful to not charge in and maybe lose it. If you can get Archery and build an Archer, you can stand outside the Encampment and fire arrows inside to wipe out the unit. But watch out that the Encampment doesn’t spawn another unit. The unit inside the Encampment will not come out to attack very often, but a newly spawned unit will be outside and will attack. I like to bring a Warrior and an Archer together so that if anything happens I have a little muscle to protect the Archer.
One of the big changes in Civ 5 compared to previous versions is that you cannot stack military units together on a tile. This matters a lot for your strategy since each unit has to be on its own tile. This means you have to think about the positioning of each unit, and that in turn means taking advantage of terrain features. If you refer back to our discussion of Terrain Types, you can see that each type of terrain and each terrain feature came with a Defensive Bonus. Looking at the Terrain Types, we see that Grassland, Plains, and Desert, which are the main terrain types you will be on, all come with a Defensive Bonus of -33%. That means you are caught out in the open and therefore have a penalty to your defense. But many of the tiles will have a terrain feature added. Hills, Forest, and Jungle all have a Defensive Bonus of +25%. So if you are on a tile that is Grassland plus Forest, you only suffer an 8% penalty on defense. Same with Desert plus Hills, or Plains plus Jungle, and so on. So if you think you may be attacked, moving onto Hills or into a Forest is good. Also it is worth noting that attacks across a river penalize the attacker with a 20% reduction in their attack strength. So learning how to use the terrain to your advantage is a key skill in combat operations.
Let’s see how this works with a Warrior, the unit you have from the start. It has a combat strength of 8. So in the early game you might encounter a Barbarian equivalent, called the Brute, but which is an identical unit otherwise, and also has a combat strength of 8. If you meet each other on grassland tiles with no features, you each have the same defensive penalty of -33%. So you are evenly matched. But the other factor is the health of each unit. This is measured as hit points, and you can see this shown in a colored bar next to the unit. If you see no bar, the unit has all of its hit points and is at 100% health. If the bar is green, it has lost a few hit points, if yellow you are starting to get into a danger zone, and if red it is very likely to be killed in any combat. So even if the combat strength is equal, if one unit has a green bar and the other a red bar, there is an excellent chance that the unit with the red bar will be killed in any combat. You can recover your hit points by resting the unit. Resting in general recovers 10% per turn, but 20% per turn if it is in your territory, and 25% if it is in one of your cities. There are other modifiers such as Medics and Faith Healers that can add recovery per turn and heal your units even faster.
Units can also earn Promotions. These add to their abilities in various ways. There is a good chart of Promotions at the Civilization Wiki site https://civilization.fandom.com/wiki/Promotions_(Civ5). For Melee units such as Warriors, the main ones would be Shock, which gives a bonus in open terrain, Drill, which gives a bonus in rough terrain like Hills and Forest, and Cover, which gives a defensive bonus against ranged attacks, such as Archers. You earn Promotions in combat. And if you have a unit that has a few Promotions, it is generally a good to upgrade it to a newer unit rather than delete it and build a newer unit because it keeps the Promotions. You do this by using Gold to upgrade the unit, so don’t neglect your Treasury!
The first ranged unit is the Archer, which you get by discovering the Archery technology and then building one. They can attack up to 2 tiles away, but only have a combat strength of 5. That means a Warrior attacking an Archer has an advantage, to so you will want to protect your Archers. They are well suited to city defense since the city helps protect them and they can drop arrows on an attacker before it can hit the city in many cases. Otherwise, it is a good idea to put your Warriors on the front lines of combat and station the Archers behind them. This is also how you attack cities early on. Use the Warriors to absorb any attacks from the city, while your Archers drop arrows into the city from behind the Warriors. Cities also have hit points, and you can see how they are being eroded by colored bars above the city using the same Green-Yellow-Red standard. But note that once the defenses are down, you need to use a Melee unit to capture the city. Ranged units cannot make the final capture. As the game goes on, your units will become better (Warriors–>Spearmen–>Swordsmen–>etc.), but the principles never change.
Naval Combat
When you research the right technologies you will discover Ships, and you can start using them in combat. The earliest vessels you will get are Triremes. They have an combat strength of 10, but are vulnerable to ranged attacks. They can clear Barbarian ships from your waters, and are good for exploring the coast lines. But they cannot travel on Ocean tiles, which are a deeper blue than Coastal tiles. They can attack cities, and as a Melee unit could actually capture them, but in practice this is rare since they would probably be bombarded and sunk. Still, if you were in some odd circumstance where your Archers had reduced the city defenses to nothing and you had a Trireme on the spot, it would work. Later on you get Caravel, the first ocean-going vessel, and you should use them to explore the rest of the map as soon as you get them. Then Privateers, a powerful ship that not only is good for raiding coastal cities, but can capture enemy ships and add them to your fleet.
There are also Naval Ranged units. First is the Galleass, followed by the Frigate. The Frigate is a powerful mid-game unit. That they are ranged means they can stand off shore and bombard units or cities on land. If you want a fun game with naval warfare, try an Archipelago map, get your Privateers and Frigates, and go out and conquer! As with land units, you can get Promotions for naval vessels. And there is an upgrade path as well. Trireme–>Caravel–>Ironclad, and Galleass–>Frigate–>Battleship.
Air Combat
This comes along late in the game, obviously, arriving in the Modern Era. Your two main unit types are fighters and bombers. Fighters are mostly for attacking other air units. They can do damage to ground units as well, but they are not really suited to that. The first fighter unit is the Triplane. It is also useful as a Reconnaissance unit as they can see 6 tiles in every direction. You can station them by a city and set them to Intercept mode, where they will respond to any air attacks from other players. The other major air unit is the Bomber. The first of these is the Great War Bomber. It is designed to carry a load of bombs and can be very effective in reducing the defenses of a city. It is weaker on defense, though, so a good strategy is to send in a few fighters first use up any of the cities anti-air capabilities, and then follow up with the bombers.
Air Units also can get Promotions from combat. And they also have hit points just like all other units. And they have an upgrade path. Triplanes–>Fighters–>Jet Fighters, and Great War Bomber–>Bomber–>Stealth Bomber.
Conclusion
This is just a very brief introduction to Combat in Civ 5. You could probably write an entire book on on all of the strategies involved, but this will get you started on the basics of the combat system. Civilization Fanatics has a section called the Civ 5 War Academy where you go into much more depth if you want to really master combat and strategies.