How to write combat scenes

Do your research

Before you even begin planning the motions of your combat scene make sure you do research on the elements involved in your fight. Are you planning on using a specific fighting style? A specific weapon? Maybe a specific type of armor? Research them. While the average reader might not know whether a .44 Magnum holds 5, 6, 7 or 8 bullets or whether a claymore is a sword best held with one or two hands, some readers do. Messing up these details can make your writing look clumsy and it'll likely take those knowledgeable readers out of the story.

Doing your research could also mean discovering techniques not many people know about and using this in your story could make a fight not only seem more authentic, it could also lead to surprising offensive and defensive moves.
For example, not many people know about the technique 'half-sword', here's the Wikipedia page on it.

Obviously you won't have to worry too much about this when you're writing fantasy as you can make up your own rules, but it's still a good idea to do some research to have at least a realistic basis for your creation. For example, you may be planning to create your own fighting style, this generally won't turn out too well if you don't take into consideration what makes fighting styles viable and great, things like stances, types of punches, effective ways of blocking an attack and so on.

Purpose of the fight

Like everything you write in your story your fight has to have a purpose. Writing a combat scene purely because you think it'll interest the reader will accomplish the opposite, as will combat scenes which occur through illogical behavior from those who do the fighting.
When you write a combat scene you'll have to take those who fight in consideration, obviously. Who are they? Why are they fighting? Do they want to fight? How do they fight?

It's important to make the character's motives clear, they make the fight interesting after all. Motives imply there's something at stake, whether it's survival, pride or something completely different doesn't matter too much, it's all relevant to the fighting characters. Without these bits of personal information you'd simply have two or more people trying to beat each other to a pulp, which generally isn't very interesting to read.

A fight can (and possibly should) reveal far more about a character than just the motives and way of thinking during a fight. It could reveal part of the character's personality, like whether or not that character can stay level headed or if he or she will be caught be the taunts of the opponent. It could reveal whether a character really is the magnificent fighter all the rumors claim to be the case. It could reveal one of the characters uses a fighting method also used by a wanted criminal, coincidence? Maybe.

A good fight scene is far more than just a fight between two people, it provides information to the reader just as great dialogue would, it advances the plot and potentially enriches the story universe through (fictional) fighting techniques and weapon choices.

Results

This point ties in with the previous one as the result of a fight is part of why you write it. But it's important to consider the results you want from a fight before actually writing the fight. If you want your hero to come out on top without as much as a scratch you can't really let the villain throw the hero through glass or smash him with a chair, despite what movies may show those actions would cause actual harm.

At the same time if you want your hero to be wounded, perhaps enough to be in critical condition, you'll want to think about how you'll plan the fight to make sure those wounds can occur in a natural way. If your hero needs a broken leg by the end of the fight you could accomplish this through a fall from great height, a hit from a hammer or from being crushed by the villain himself. But these things can't come out of nowhere. The height difference has to be there early on, the hammer can't just suddenly be there out of the blue and the villain has to overpower the hero before he's able to crush that leg.

Just the results

Sometimes you don't have to write a combat scene at all, you merely have to show the results. This can be incredibly powerful, sometimes more powerful than the fight itself could've been. For example, say a class bully and whoever is being picked on have arranged a fight. Everything points in the direction that the bully will completely crush the poor victim. You write the chapter until just before the fight starts, before the first punch is thrown. Write how the bully is confident, how terrified the victim is, the victim thinks this is the end of everything, there's no hope left and then the chapter ends.

The next chapter starts with the victim, beaten up and bruised on several places. Everything indicates the bully did indeed crush the victim. Then the bully enters the scene, beaten up far worse than the victim, it's surprising the bully is even able to stand.
It's clear by now the fight didn't turn as you'd expected from the end of the previous chapter, but the details of how the fight was won are completely unclear and will leave the reader wondering what did happen and the reader will thus continue to read on to find out. Did the victim win on his own? Did somebody help and if so, who?

This method isn't always the best option, sometimes you need to write the full details of a fight as it is happening purely for the enjoyment and fulfillment of the reader or because it supplies the reader with important information. The fight scene in which the hero finally gets to exact his vengeance upon the villain for killing all his friends isn't something you'd want to skip. You can't skip to the next day with the villain buried underground, the reader has to know what happened and how it happened, the reader needs to be able to feel the satisfaction (or perhaps disdain) the hero feels while defeating the villain.

Do not overwrite

So it's time to actually write the fight scene. The perhaps single most important thing to remember while writing your fight is to not overwrite it, leave as much to the reader's imagination as possible. There are quite a few elements to take into account to accomplish this, which I'll cover in more detail now.

Outlines

To allow the readers to imagine the fight and create the choreography on their own you'll have to provide them with the information to do so. Where are the fighters? What weapons are they using? How are those weapons used? Do they have armor or other forms of protection and cover? Are there other elements which play a role later in the fight, like a crowd or potential weapons laying around?

Once the reader has the information needed to imagine the fight you won't have to mention them again. A sword may change hands, but don't tell the reader the exact position of the hand on the hilt or whether the hand is gloved or not, keep the details short and move on with the action.

Pace

Fights are fast and you'll have to reflect this in your writing. You do this by using short and simple sentences. Longer sentences can be used when slower actions take place, like a stand of between two sword fighters, both of which are eyeing the other to find an opening while they pace around in circles.

Of course not all sentences have to be short, doing so could make the fight annoying to read. You'll have to find the right flow fit for your fight, some fights will require many short sentences in succession to replicate the quick punches thrown after each other or the fast sword strikes, other fights have a slower fighting technique. You'll also want to keep in mind that not all fights are one continuous attack, fighters change positions, try to find a different opening or step back and try to keep their distance while figuring out the best way of attack.

Another elements which helps with pace is starting new actions on a new line. For example:
He swings his sword down.
She blocks.
She strikes back and aims for his throat.
Instead of: He swings his sword down. She blocks. She strikes back and aims for his throat.
The first example keeps the reader on edge, every action is separated which makes the action feel more natural, dynamic and sudden, rather than reading everything in one long paragraph where everything almost merges together and seems to lack a pause between actions, which makes everything feel less sudden.

Grammar

Changing the grammar you use for combat scenes will also help a great deal in making everything feel more vivid and exciting. There are 3 main points you'll have to keep in mind, the first is don't use passive sentences.
A passive sentence is a sentence in which the subject does not perform the action, the action is performed on the subject. For example: 'His stomach is pierced by the beast's sword.' By turning it into an active sentence you get: 'The beast pierces his stomach with its sword.' The active sentence sounds more natural in the overall flow of the fight and, similar to using pace, the action sounds more sudden.

Another point to keep in mind is to use verbs instead of adverbs when it simplifies a sentence. Adverbs can make a sentence longer, which is generally not what you want in a fight scene. For example: 'She hits him very hard in his face' is better written as 'She smacked his face'. 'The beast throws him to the floor and points mockingly at him.' is better written as 'The beast throws him to the floor and mocks him.'.

The third point you have to keep in mind is to simplify your grammar. Don't write 'From a nearby crate he grabs a rod and swings it at the beast.', write 'He grabs a rod from a nearby crate and swings it at the beast.'. The action flows much better this way.
Simplifying your grammar also means choosing simpler words, action is fast so the sentences have to be fast as well. Don't write 'He sidesteps the attack and retaliates with a vigorous blow' when you can write 'He dodges the attack and strikes back with a mighty blow.'
Do note that this doesn't mean you can never use longer words, sometimes you need to use them to express something the right way. 'He strikes with overwhelming force' doesn't have to be changed into 'He strikes with great force' as it doesn't express the same magnitude of the strike.

Perspective

Perspective may seem like an obvious point to keep in mind, after all your entire story is written from a perspective so why would a fight be any different. But perspective is especially important in a fight scene. In general a fight scene shouldn't be written from an objective point of view, it's far more difficult to express the excitement of the fight this way. Instead it's best to pick one of the characters as a view point, which doesn't have to be a first person view point, and let the reader experience the fight from that perspective.
Alternatively you could use the perspective of a spectator, this works best if that spectator has a personal connection with one of the fighters.

Letting the reader know a character's thoughts really helps bring a fight to life, it can make it incredibly exciting, like when the hero manages to defeat the odds after all, or oddly morbid, like when the point of view is from the vicious and cruel antagonist who takes joy in hurting others.

Obviously you'll still have to pick a perspective that fits the rest of your story, if you use a first person perspective throughout your entire story it would be odd to suddenly change to a third person perspective for a fight, and vice versa.

Use the senses

This ties in with my previous point about perspective. In a fight it's far more important to use the senses of a character during a fight rather than describing the fight and everything around it yourself. During a fight a character won't notice a lot, every sense is focused on the fight.
At the same time using sensory information helps the reader relate to the character more than a description would and it helps making the reader almost feel every punch the character feels.

For example, say the hero is wounded you wouldn't write 'His clothes are drenched with blood, the red fluid drips from his fingers and stains the fresh, white snow below him.', instead you'd write 'His bloodied clothes are sticking to his body like a second skin, they're soaking wet and give of a strong metallic scent. He can feel droplets of blood running down his arm and drip off of the tips of his fingers.'
While the first sentence isn't necessarily wrong, it keeps a distance between the reader and the character. The second sentence closes that distance and describes everything in a way the reader can relate to. While hopefully nobody knows what it's like to be covered in blood, many people do know what it's like to wear wet clothes and what a water droplet running down your arm feels like, this helps enormously with imagining what the character feels in that moment.

Keep it original

Another point which may seem obvious is to make sure every fight is original and unique. Even when the same two characters fight with the same technique as the previous time the next fight has to feel different. When fights are too similar not only will they be less memorable, you also make them predictable and thus boring to read.
It's also unrealistic for two fights to be similar, even if all the elements are the same in both fights. When the same two characters fight another battle they would've learned from the previous fight and approach this new fight differently. If the hero fights a new opponent the same techniques used on the previous opponent may not work as well, maybe this opponent learns quicker and knows how to avoid those techniques or maybe this opponent knows a technique which counters that of the hero.

Non-human fighters

A final point I'll leave you with is to make sure that even when you're using imaginary creatures in a fight it's best to add some form of realism. Use real creatures which are similar to your fictional one as the basis of how that creature can move and fight. For example, a centaur may have the fighting capabilities of the torso of a human, its body is that of a horse and is thus restricted to the movements of a horse. Horses aren't as quick and agile as humans when face to face in a fight, but they can easily outrun many other creatures.
This same logic can be applied to all, or at least almost all creatures. An ogre can be seen as a large, bulky man, a troll can be seen as a lean, agile man, perhaps even as an ape if its limbs are long, and so on.