Hi WOW, my name is Tod, and I'll be your official greeter from the "AW is like a movie" camp. If you get really positional (maybe even draw a map) there can be a lot of acting under fire and reading the sitch. Even reading the opponent if it's close-range combat.
Just remember we're focused on the characters, right, this is not like watching a live battlemap with a bird's eye view. So we follow the characters around and we do the conversation thing. Set each scene descriptively. Describe some bad thing going on. When they do something, they're doing it. When they look at you, set them up with a soft move ("you see them moving into position", or "you realize you are surrounded", or "there's a sniper on the roof - maybe more" - followed by what do you do?). If they fail a roll, the typical Hard Move will be to Inflict Harm as established, but it could be something else.
If this is a large combat scene (explosions, vehicles, whatever), "Barf Forth Apocalyptica" temporarily becomes "Barf Forth the Hell of War". If gangs are involved, use the gang harm rules. They will tell you how the overall battle ends up, but in the meanwhile you can push toward it one detail at a time. Use the gang harm rules to guide these cutaway flashes of hell.
Suppressing fire is not a move, you just do it (of course you can always make up a custom move for it), but it
can be a way of "helping" someone else do their move.
When the battle is over, whatever's left will become more Apocalyptica to barf forth. Nice how that works. :-)