Before I get into this one, let me establish something that wasn't obvious to me when I started to philosophize about storytelling. The point of describing a fight scene - or any action scene - in the first place is to let the reader envision it. I say 'let' because if you just skip over the scene ("We fought and I came out on top"), the reader is effectivly prevented from envisioning it; if they care enough about the story to be reading it, they're just going to want to go on. Stopping their reading to imagine a fight would kill the enjoyment of doing so. That's why this has to be the author's responsibility. With that, here are a few points of advice I can give, despite being far from an expert myself:
This flaw is constant in Attack on Titan. The worst instance was when they're trying to convince the soldiers that Eren's not a titan; after Eren tells Armin that he has 15 seconds to make his decision, the amount of conversation between then and when he does couldn't possibly have taken place in less than a minute. It was bad enough to make me laugh out loud, despite how great the rest of that scene was.
As far as fight scenes in particular, there are three main types as far as I'm concerned: fisticuffs, swordfights, and gunfights; and each one is very different. And of course, writing a realistic fight scene is very hard if you don't know much about the relevant kind of combat in real life. This is problematic insofar as the reader does have the knowledge you lack, since if they don't they won't know you're being unrealistic. And obviously the burden is alleviated by less detailed choreography (see below). But only partially.
That's why I think it's such a good idea in fantasy novels to create a radically new combat system: no reader will be more qualified on it than you are. No one in real life has any first-hand experience and you've put a lot more thought into the ruleset than anyone else has. Of course, that doesn't completely solve the problem - you still have to follow basic ideas of physics and human intelligence, like making sure characters who are supposed to be experts don't forget to use an ability or technique that you've taught the reader is a thing in an obviously prime situation for it - but it's a big help.
Regarding fisticuffs in particular, I've gained a little bit of experience recently, and if there's one thing I've learned it's this: it's a lot less punching and kicking and dodging than I used to imagine, and a lot more grappling. Especially if you're fighting for serious injury - you know that a punch to the chest or a limb might hurt a bit, but it does basically nothing in terms of actually incapacitating your opponent. If that's your characters' goal, and they're not stupid, they should know that the main way to do that without a weapon is trauma to a vulnerable body part, such as the head.
Another thing I would say as a near-novice of the art is to use the environment. Be mindful of nearby tables or other hard objects. Being pushed into one can be a lot more injurious than being punched.