It's weird to not see descriptions of the actual mechanics, I mean for me, that is one of the initial angles by which I try to understand a game.
So there actually are mechanics mentioned above, they may just not be as easy to spot as something like task resolution in D&D. I mentioned several above, but I'll pull them out and highlight them again.
*
XP TRIGGERS - Again, in terms of prep, you're thinking on provocative situation (circumstances, pressure-points, developing NPC actions/impulses) and you're asking questions directly to the players about the same. Each PC has two attributes that have been highlighted (cool, sharp, weird, hot, hard), an Hx rating with people (relationship value between +4 and -3), and thematic moves (typically a playbook move) that say "mark xp" when triggered. You've got these mechanics in mind when investing the game with life by (a) making soft moves with this stuff and then possibly (if the play of the game reveals that there is "meat on the bone"; interest + developing conflict) (b) systemetizing them into actual Threats.
*
THREAT CLOCK - You've got 4 wedges. You make a soft move (telegraph potential badness happening if not addressed). If its not addressed, you fill in a wedge and something happens (just like a soft move turning into a hard move at "the local level" lets call it). If the whole thing fills, it goes "boom" and whatever happens, happens.
*
THREAT CUSTOM MOVE - The great thing about PBtA games is that the move structure is very well engineered and transparent. Its a straight-forward deal.
Thematically appropriate trigger in the fiction (eg
"when Motley Marion lays her hands on you in The Pit roll +weird") > Roll 2d6 +mod > 10+ = you get what you want, 7-9 = you get some of what you want or all of what you want but with a cost/hard choice, 6- = things go bad.
So you have a Threat. You have a thematic trigger for when the PCs interact with the threat (this might be interact period or interact under particular circumstances...it just depends upon the trigger). Dice are rolled. New gamestate and fiction post dice rolled (possibly with a choice in the middle if the result is 7-9).
These are all both (i) areas of GM prep and (ii) (important) game mechanics.
If you're taking on being an MC in AW, be very familiar with all of the above. Know it well and ruminate upon it between sessions (and systemitize Threat stuff if play warrants it).