The mechanics of a fight scene refer to the actual fighting itself, and the accuracy with which it’s portrayed. 

There’s not really a whole lot to say here. Obviously, the more authentically you portray a particular style of combat, the more immersive your fights will be. With that in mind, any time you’re trying to show the reader something you’re not intimately familiar with, you’ll probably want to do some research. 

I personally recommend going to YouTube and searching “how to fight with X”, with X being whatever your weapon of choice is. Or “how to use X,” or “X martial arts.” Something along those lines will probably net you good results. Just make sure you check the comments section to make sure they’re not a fraud. It happens more than you’d think. 

Backing up a little, note that I say “authentically,” not “accurately”. 

When constructing an immersive experience, authenticity matters more than complete accuracy. I say that knowing full well that pedantic nerds in comment sections the internet over will vehemently disagree, but I have two counters. 

First, yo mama. I will not clarify further at this time. 

Secondly, crafting an experience for a reader, or in the case of film or games the viewer or the player, is more about making them believe the world is real than it is about getting every little detail exactly right. 

Take the movie Fury, for instance.  

If you’re not familiar, Fury is a WWII flick about Brad Pitt leading a crew of ragtag misfits across Germany in a Sherman tank of the same name in the waning days of the war. It’s grim. It’s gritty. It’s one of the most immersive movies about a tank crew ever made. It’s also not terribly accurate when it comes to the little details. 

Were the Americans really so desperate for replacements that they’d press a barely trained typist into service as a wing gunner on a tank? I’m sure it could have happened, but by the end of the war, the American military had over 12 million servicemembers under arms. They probably could have found a properly trained assistant driver if they wanted, but the story was better served by an ignorant and innocent surrogate for the audience. Not accurate, but it helped the story feel more authentic. 

Same thing with the battle against the Tiger at the end of the movie. Not only were the tactics on both sides completely wrong, but the scene relied heavily on the old adage that it takes 5 Shermans to kill a Tiger. That’s not strictly true, it’s just that American tanks tended to move in 5 tank platoons. If you see an enemy tank, you’re not going to carefully meter out the exact number you need to defeat the threat. You’re going to throw everything you’ve got at it and bury the fucker in shells. 

Speaking of shells, the 75mm and 76mm shells are seen bouncing off the Tiger’s armor. It’s true that the Tigers were tough, but it’s equally true that more than one was killed because Sherman drivers got fed up and started pelting the damn thing with high explosives until the concussions turned the crews’ brains into soup. American tankers knew the limits of their machines and found ways around them. They didn’t just shit themselves whenever the Germans threw a big cat at them.

In reality, that fight wouldn’t have been nearly as close as it was. That’s not very accurate. But the desperation, the stakes, the sense that no one was safe, that made it feel authentic. They really captured the sense of a desperate struggle painted in shades of moral gray. The audience might not know the minutiae of tank combat in the World Wars, but they sure as hell know a last stand when they see one.

Speaking for myself for a moment, I'm not above fudging details in other to tell a better story. I'll simplify things like how to engage targets with night vision because taking the time to explain the whole process would kill the flow. But by including just enough to make it feel authentic, someone who doesn't know any better isn't likely to notice the fudge. 

If you have to choose between authenticity and accuracy, go with authenticity. That said, authenticity requires at least an element of accuracy, so this is where research comes in handy. 

You don’t have to learn every single guard in Fabris or Capo Ferro to write a rapier fight. Your audience probably won’t understand if you tried to use all the technical terminology without explaining anyway, and that would drag down the pace. But you can still give the impression that a character is a master, and for that, a little bit of jargon could go a long way. 

You could, for instance, find one or two key moves you want to use, learn them well enough to describe them in detail, and figure out how to use them as the centerpiece for the fight. Maybe your MC has spent a lot of time training a particular technique. Setting up to allow them to use it, and then letting that end the fight, is an excellent way to pay off narrative stakes.

You can also study the time period your story is set in, or a close analogue. Little details, like clothing, diet, whether or not the streets are paved, all of that can influence the outcome of a fight. You can also use them to help build authenticity. You don’t have to bury the reader under fine details, but you can use them to paint a picture of the world and make it feel like something that real people live in. 

This is one of those things that takes time and experience to master. If you really want to do it well, you're just going to have to keep trying and failing, and learning from those failures so you can try again. It also helps to read and watch movies set in the period you're working in to try to get a sense of what it should look feel like. Conveying authenticity is a skill, something that has to be learned. It's also a convenient segue into the next section.