I take it for granted that I know how I run and have been running my games for a few years now according to the "free kriegsspiel/FKR" (henceforth "ultralight") approach. For almost a calendar year since this concept has become increasingly vogue across the interwebs, many earnest folks have raised repeat questions not about "what is this?" but "how does it actually work?" At the risk of being overly ironic, think of this post as an introductory rulebook to a style of play that assumes a rulebook is patently unnecessary. I'm going to make this quick, because that's something I especially appreciate about this method: it's fast, it's intuitive, and it only needs a little nudge to get going.
Disclaimer: This is how I run my games. This is not "how it always works." It is a (hopefully clarifying) example. The approach here is a varied spectrum. Two referees adopting similar styles may yet produce very different tables. This is, of course, how any two different people running any two different games will pan out, but it's worth stating here since there is not, in fact, "one way" to adopt this method. There are various preferences, emphases, and relationships to consider. So, to reiterate, here is how I go about it.
SETTING UP THE TABLE
Numbers don't add up to a game. Again, we're all operating a fictional world together, one which we agree "makes sense" internally. In this way, we're less interested in quantifying characters with statistics or numbers as we are with keywords or descriptions. I have a much better grasp on what a "strong" person is like than what a "STR 18" person is like. If we're playing Primal (to continue our example above), a character is likely a talent/skill combo. Let's say you're "agile" and "good with tools." These are helpful distinctions for the player and me as the referee, and beyond that, we'll assume the character is average in everything else.
Give information and eliminate ambiguity. I am convinced that I sign up to run games because I am always hungry for player agency. I want to be as surprised at the table as the players who don't even know what I may have prepped. That is, I make puzzles, traps, and encounters without a known solution, so that the players don't need to press one specific button to progress. Instead, I load them up with the information they could reasonably know (including, say, something someone "good with tools" would recognize while others wouldn't), then see what they do with it. If they can know it, they should. It improves the experience for everyone present.
Tools rather than rules. Rules are not bad or dumb. Nor are dice. These are panned caricatures I've seen crop up aplenty since this form of play became more well known. Rules, however, exist here in service to play, not the other way around. That is, I might decide there is a best practice for a certain element in our setting, perhaps it's a magic system or crafting or social prestige. I can soldifiy a consistent ruling into a rule, use it when it makes sense, and perhaps drop it later when it doesn't. I tend not to use many player-facing rules in practice, though I enjoy leveraging random tables, overloaded dice, and the like.
TAKEAWAY: Everything comes back to the common sense ruling based on the setting. If a player wants to leverage the world as we understand it, let them. I trust you in good faith. You trust me in good faith.
Every book, movie, and game product works. My RPG library is infinitely more useful now with the ultralight lens than otherwise. Everything is fodder for any game. Rather than tying setting strictly to a system, I can graft inspiration, flavor, and even tools and guides from one medium and plug it into what I'm running. Any source is gameable.
There is no right/wrong, pure/tainted method. Some ultralight referees are not only diceless, they're total improv artists. No random generation, no prep, nothing. I definitely can't do that, nor would I like to. I leverage my zounds of random tables and a few stalwart tools, but even when I go diceless in play I still roll as a tool for oracles or content. The spirit of this approach is trust and ease of rulings. How that functions from table to table will differ.
It can take some getting used to. Experience dismantles preconceptions. Approach a situation and then try it without a hard rule. See if it works for you and your friends. There is no problem with playing the same game session to session even if a lot of the guts of that same game change between meeting. To quote Wizard Lizard, "Play revolves around the conversation -- Referee describes the world. Players ask questions and say what they want to do. Referee decides what happens, based on what would make sense in the world. Adventures happen."
You might not like this form of play. And you don't have to. What matters is that if you simply aren't interested in super-stripped-down "systemless systems" which are often showcased in this mode of play, skip it. There are excellent games, some of which are almost as lean, that still allow more of a flex on mechanics, mini-games, and numerical crunch than you'll find here.
ANECDOTAL TAKEAWAY: I've mentioned this a time or two before, but the more I play pared-down and diceless/semi-diceless "ultralight" games in good faith with my young son (almost six years old) the more I enjoy how great the approach is. No cruft. Nothing in the way of talking things through. Honestly I find MORE realism and sincerity of action and intent than I've experiened in years of running anything crunchier. It's collaborative storytelling but grounded in earnest ripple effects of actions. That's the big difference from story game concepts, I think, in that the ultralight sandbox is much more about taking the game world at face value and treating it like a real, breathing place where anything goes but everything has consequences, rather than THIS must happen or THAT should be the outcome. My five year old gets it. We all can as adults, too.
If you're looking for examples of these games put together more formally than a homespun dining room table conversation, I heartily recommend the following (among many others):
24XX by Jason Tocci
Blood of Pangea by James & Robyn George
Cthulhu Dark by Graham Walmsley
Landshut by Norbert Matausch
Messerspiel by OZ
Revenant's Hack by Sigve Solvaag
Skorne by Dreaming Dragonslayer
I'm also partial to Any Planet Is Earth and Galaxy Far Away, of course...