It's kind of boring.
In books, movies, and even a few videogames, fights rarely take place in a static environment. They move from place to place, characters duck and weave around different obstacles, and things get grabbed to use as impromptu weapons or improvised distractions. In a life or death situation, it's more than just moving until you're five feet from your enemy then rolling greatsword attacks.
With the chaff out of the way, let's get into the wheat of things. I like a lot of the ideas presented in Fate, but when I ran the game they never really came together for me. However, a lot of those ideas can be ported to other systems, sometimes seamlessly, due to the narrative nature of Fate. For example, let's take a look at a fight scene. How about a bar brawl? The rogue is cheating at cards, the barbarian is being obnoxious, and the bard may have told the wrong joke to the wrong person. Now weapons are being drawn and characters are going to come out swinging.
Before we roll initiative, let's take a look at the scene. Identify three things about it. For the purposes of this example, let's say there are empty tables where people were previously sitting, mugs of ale left unattended, and someone passed out drunk on the floor. Grab an index card or whatever you use to take notes and jot those down, let the players know about them. These are your primary scene aspects.
Let players use these scene aspects how they wish, and adjudicate them how you want. If the rogue wants to splash ale in someone's face before going in with their dagger, you could rule that (in 5e rulings at least) as an object interaction, allow the thug a saving throw against a DC (10 is generally a good guideline, or use some other way of adjudicating it), and confer advantage to the rogue if the thug fails. Tick that aspect off. If the rogue wants to keep using their drink-tossing trick some more, either give advantage to the thug's save or just tell the player they'll have to look for another way to trick the thug. That's where creating/discovering an aspect comes in.
To create or discover an aspect, just use the same toolset the game you're playing gives you to resolve ability checks. If the player wants to discover, create, or modify an aspect, just have them roll an appropriate ability. The bard's player, for instance, could ask if there was anything nearby he could grab to use on the thug cornering him. A perception check could have him discover a pie that was recently set to cool, just within arm's reach. An aspect has been created, and the player now has ideas to utilize it. One improvised attack roll and a scalding hot fate for the thug later, the bard is ready to join the fray.
Now that was a lot of words for what is basically just writing down short scene descriptors on an index card and letting players use them! Granted, they could already be doing this, or they could just ignore it all and keep moving and attacking. As always, you have to see what works for your table.
