Make sure the group understands the basic dice rules - FORKs, Help, Advantage Dice, Artha, etc. Usually, you can just start playing and get people going into a session and learning that before you want to touch the advanced mechanics. Just about every time I read about someone's game failing is because they ignore the instructions in the book to play with the basic rules and get comfortable before digging into Fight!, Duel of Wits, etc.
"No plan survives contact with the enemy". This is pretty much the theory that describes scripting. To be sure, in "real fights" no one is locking themselves into a set plan and then carrying them out. What scripting does is create situations where you get the chaos of a fight - sometimes you both end up on the ground under the table and honestly you wouldn't have planned for this to happen, but it did somehow.
Burning Wheel does this by having you pick your actions in 3 Volleys. So does the enemy. You reveal them at the same time and some actions work better against others - which is where it helps to strategize and consider what the enemy is likely to do. Good choices can allow you to win even though you may have weaker combat stats all around. Player skill in tactics matters.
Weapon reach matters - if you have a longer weapon and keep the opponent at a distance, they're going to have a much harder time hurting you, if you have a short weapon and get up close on the opponent, they can't hit you as well. This also means being willing to kick or push someone if they get into your guard might be useful, or pulling out a dagger for close in work, or throwing an object to win a reach situation.
The most obvious moves are Strike, Block and Avoid. They basically do what's on the tin. Block is useful because it can give you advantage dice or force the enemy to lose an action if you roll well enough. Avoid defends against ALL attacks, and it uses your Speed, which is usually going to be pretty decent. Strike doesn't just have to be with the weapon - it can be with a punch or kick, or your hilt of your weapon for close in work.
The next easy to understand actions are Push, Lock, Charge, and Throw. These usually either knock down an opponent, knock them down and do damage, reduce the dice they can use, etc. These give you advantages to follow up with, though clever use can involve pushing someone over the edge of a balcony, down some stairs, or into a bonfire. You know, fun things.
Physical Action usually takes 2 Actions, and it's the catch all for doing a lot of things - slamming the door halfway on the enemy's arm, grabbing the curtain and wrapping around their head, pulling off their helmet so their head is unprotected, etc.
Other actions are more advanced and we can deal with them later when you've got those down.
Strategy and teaching
As the GM, script your character's choices before the players do anything. You may want to have a couple of common scripts on hand you can just pick ("Oh, this dude is sort of aggressive and stupid - Charge, Strike, Push, Strike" etc.)
Then you can help the players with picking out their script choices - since yours are already picked, it doesn't matter if you know what they're choosing at this point.
Start by pointing out obvious considerations - like reach. "If you win the positioning test, they'll be at +3 Ob to hit you, which means you can go all out with little worry of getting hit. On the other hand, if you fail it, then you're going to have a hard time hitting them..."
"Why not Strike-Strike-Strike?" will be a question. Point out what happens if a) someone gets a good Block in and then you're left open, or b) both sides Strike simultaneously. "You probably won't get killed, but you can get laid out for a month recovering from your wounds... can you afford that?" If their armor is good, maybe that's a worthwhile risk, if not... well.
After they're chosen, run through the first Exchange. With each roll, ask them if there's a FORK that can be applied or check for Advantage dice. If some particular combination of maneuvers leaves someone open, point that out. If anyone fails a Steel Test, point out what that means for the next X number of rounds.
Explain why you chose the Maneuvers you did for the NPC(s). This can be "Well, this guy's not too bright, he's going to choose straight forward things." "This is a predator, it pounces (charge), pins you down (lock) then goes for the throat (great strike)." "He's a cautious guy, he's going to defend and see what kind of fighter you are before deciding how to take you out." etc.
Exchange 2, considerations
Now you can bring up other things to consider:
The Fourth Action
Most characters will be working with 4 Actions. That means the "2nd action" on one of the Volleys is more likely to score a hit - the opposition will probably have a 1 in 3 chance of guessing the correct volley to defend on if they're going to try to defend against it. It makes it an excellent place to put an attack in, or a setup for an attack.
Disadvantage for Big Success
Disadvantage adds successes to the opposing side. So if you get the opponent stacked up with disadvantage, you get free successes to throw on your action. That's a good reason to knock folks down, tangle them up, etc.
Tests for everything
Each skill/stat can only get one advancement test from this whole Fight! If you want to game it to get the most from it, you'll want to use as many different skills/stats as possible to each get them one.
Steel Tests win the Fight!
Getting the opponent stunned is where you go in and mop them up. The most common way to do this is to score a Light Wound or better. But some things like magic, or pulling off something very surprising can also trigger a Steel Test.
If a PC has a shield - explain Block and Strike. If someone has really high Power, let them know a little more about what Lock and Throw can do for them. Etc.
End the Fight Early
If the enemies take wounds, they'll probably bow out/run/surrender pretty quickly. Don't start with a life/death battle, start with something where being driven off/captured on either side makes more sense. If the heroes take wounds, it might simply be "And don't come here again or we WILL kill you!" threats.
Tally up the Advancement tests, don't forget to add situation based Steel Advancement as well. Take a look at the wounds, figure out what kind of medical care is needed. Take note of any choices people could have done differently or worked really well. Acknowledge if someone had a good plan but a bad roll - "Wow, that would have been great but the dice were crappy this time."
If the enemies are still around, consider a social test or Duel of Wits - naturally with a large advantage to the victors.