OK, so, full frontal caveats, my playing OSR/D&D as story now, even in part, is very much a personal thing for me. I don;t have a guidebook or a set of rules about how to make that work. So I am running a fantasy sandbox using Black Hack 2E, and I am trying to run it as story now as possible. So I'll try to explain how that works for me.
The first hurdle for running D&D or OSR as story now is that the mechanics really don't help, and in places even push back against it. This is less of an issue with rules light OSR games than it is with D&D (or Pathfinder, I'm afraid). Most story now games have a limited success mechanic, or a success with complications mechanic. When a player rolls a result like that it's a signal for the GM to 'make a move'. In my case I'm using the standard AW or more specifically Dungeon World keeper moves. The problem is that there's no mechanical place to insert that move. So what I tend to do is take the aggregate of the party rolls in a round, or in a situation, and use that as a bellweather to see if I'm going to make a move. If things go badly, I'll add complications, if things go well, I won't.
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So when my example game started I had a very traditional amount of prep done for where I thought the player were going to go. I had dungeon locations, factions, maps the whole schmozzle. As players are wont to do, they didn't go that direction at all. At which point I thought, ok fine, I'm going to run this like DW and see how it goes. I'd done this in bits many times, but this time I was going to play it to the hilt. So I wrote up a couple of fronts (the DW version of prep, which is minimal as all get out) and I just let the players roll. As they went places and did stuff I reacted and adjudicated. I made up the occasional new map, as PbP kind of requires some props, but that's it. Even now, the party is in pretty critical danger, and I'm not sure what's going to happen next.