In my initial "Definitions of FKR" post there is a lot of flowery language and great explanations of ideas which I think it is great. Though, re-reading it and after more experience it all sounds way to theoretical and may be confusing. I am going to list various aspects but they are not in any particular order.
The first thing is that playing games FKR style or FKR games are designed to be high trust or played with an high trust mindset. This roughly translates that the players trust the Referee to be fair, knowledgeable, and that the Referee is going to make clear consistent rulings. To condense this further, the Referee has a lot of authority to make unilateral decisions without necessarily failing back on any published rules.
The second thing is that the Referee tracks a good amount of the player focus stuff. This could be magic points, hits, gear uses, and so on. By doing this, the referee creates an environment where the players spend more time immersed in the fiction.
The third thing is that generally, the style is played with little rules. No 600 page rule books to be found as far as the eye can see.
The forth and final thing tends to cause a lot of discussion and is something that causes a lot of confusion. FKR style games tend to be rules light and the players do not have access to whatever rules or ruling they are out going to experience during the course of play with the minor exception of what is needed for character creation (and to make meaningful decisions during that process). So, with that being said, it is possible to run Pathfinder, 5e, or even GURPS in an FKR style but I do not know why a Referee would want to do that to themselves.
Here is where the confusion comes in. People will argue that Dave Arneson (and others) did not have rules when he ran his games but that is not the case. It is well documented that Arneson handed over 18 pages of rules to Gary Gygax that would be used to help design the original release of Dungeons & Dragons. Though, whatever rules or rulings Arneson used, he kept to himself and there was no players handbook that the players had access to. Hence, this is where the high trust aspect comes into play and the ye olde reference to the invisible rulebook.
Another point of contention that this forth aspect causes is that there is a lot of rules discussions regarding this style of game or play and it tends to frustrate the veterans and other people who have a lot of experience with this style of gaming. This has caused some of the veterans to step away from those conversations and those spaces.
This situation just comes from a lack of understanding of the play style and a lack of comfort from people who have little or no experience of the play style because they want guidelines or sets of rulings to help them on their journey. That is where the barrage of rules questions come from. It also does not help that a lot of FKR products do not offer much in referee guidance outside of resolution mechanic and some character creation. There is no problem with people seeking rulings that they can use for their games or to use until they are comfortable to create their own.
Circling back to the high trust aspect of FKR and the higher responsibility of the Referee I am going to try to smooth out the misunderstandings, wrinkles, and try to assist new Referees wanting to run games in this style.
So, as a Referee for this style of game, you are in charge of creating a high trust environment, conducting research, and separating the players from the rules so they can be as immersed as possible in the experience. So, the referee should come to the table prepared with some baseline rulings, campaign information, and their handy dandy notebook. Depending on the comfort level of the referee will determine how much rulings they bring ready to go in their notebook and how much on the fly rulings they will make during the course of play. That is why it is important to have the notebook and to MAKE SURE TO WRITE IT DOWN so the Referee can make the exact same ruling or call the next time and the time after that. Consistency is key - hence the high trust aspect.
For an example, in a game that Arneson was running someone decided to throw a fireball and the response was what? The answer to the what was well, I am a wizard and that is what wizards do. So, on the spot the ruling for a fireball was decided and was written down in the notebook.
As for research? Yes, it is important as the referee to take time to research things the characters in the game talk about, are interested in, or discuss. I am reminded of a story where Gary Gygax was running a game and there was a 16 year old high school kid at his table. During the session, the 16 year old announces that he hits the opponent with ??? (I do not know what the word is - but it was some fancy word for some fancy polearm) and Gygax had no idea what that was, but he did not let the 16 year old kid know that. So Gygax gave it a damage rating, wrote it down in the notebook, and then the next day Gygax went down to the library and read through a historical book on medieval weaponry. This is probably one of the reasons why there is a listing for every can opener on a stick in some of the books. Regardless, the point still stands. Referee's need to do their research and use their notebook to make sure their rulings and how they handle situations stay consistent.
That is the style of and how to run it on the referee side. The players responsibility in this is to trust the Referee and let go of all modern gaming sensibilities.