So I have the Big List of NPCs, the Random Mission Generator, the List of Organisations, and the Relationship Hexmap. This is the raw material from which the game emerges. It's important to keep this vision of "game as emergent" in mind when running any sandbox game, as I'm sure you'll agree.
Anyway, how does it work in play? Like anything, it needs a bit of work from the GM and a bit of work from the players.
The GM's job is to use the raw material to improvise. This is more than just rolling on the Random Mission Generator. It needs him to constantly think about what's going on throughout the city, what the various actors are doing, and what the consequences of the players' actions are. This could be as simple as "the players have robbed a bank so the police will be investigating" or as complicated as "the players have introduced £2,000,000 worth of heroin onto the street - how does that affect the state of play between the different drug gangs in the city?" The Big List of NPCs and the List of Organisations help with this, because they provide motives for the different actors which suggest how they will react.
The GM also needs to be good at improvising. The nature of a non-linear game is that it's surprising, and a city sandbox has fewer anchors than a traditional fantasy one: there is no hexmap and there are no random encounters (at least, not how I run it), two things which are natural fulcrums for a GM to riff on. And the players are not constrained by geography, if it's a modern or futuristic setting: they can travel freely and quickly, wherever they want. This means the GM needs to be on his toes all the time - the players could do decide to do anything at any moment, and he needs to be able to make stuff up on the fly in response.
The Big List of NPCs naturally helps, here. Perhaps the players decide they want to get their hands on some horse anaesthetic? Check the list of NPCs, find a vet. Turns out somebody who they know knows him. Bingo. But it also helps to let the players know that you're making stuff up. I'm never afraid to be obvious about the fact that I'm making something up on the spot. An example from tonight's game: my players went to a bar to try to meet a politician rumoured to drink there. I had no idea they were going to do this. I needed to make up prices for champagne, the names for the politician's friends and floozies, the name of the barman, and several other things. I was perfectly open about plucking names from thin air, and rolling a dice to see how many drinking companions the politician had. They know it's a game: you're not fooling anybody by pretending you have it all planned out.
Correspondingly, the players have a big role. They have to be active. I'm blessed with really good players in this regard. They have ideas. They brainstorm. They want to interact with the setting - to meet new people and make contacts, to move things forward, to act. They are an engine.
But their actions are also food for me as the GM. By going to that bar that I wasn't expecting to go to, I now have four new NPCs for the Big List of NPCs. And each of them has a motive, a reason for existing. More flesh is added to the setting, and who knows when one of these NPCs will become relevant again?
Players also have a tendency to take a "bull in a china shop" approach (I'm sure this holds true across every game group that ever existed). To put it simply, they fuck things up, in good and bad ways. And their actions also feed into the setting: they attract the attention of the police, they make enemies, they kill people, they fundamentally change the economy and the physical make-up of the city.
All of this is gold for the GM, and it becomes a self-perpetuating process: the more the players do, the more they flesh out the Big List of NPCs and the List of Organisations; and the more this happens, the more stuff there is for them to do. Over time, the setting becomes far more than the sum of its parts.
What this means is that, the longer you play, the less time it takes for the GM to prep. Things begin to take on a life of their own. The players act, and their actions have consequences, and those consequences force the players to act, and that results in more consequences... and so on and so on and so on like a snowball. While the time investment before play began was big (say 5 or 6 hours total), the GM now spends about 30 minutes a week preparing for the next session - just statting up anything that needs statting up, ruminating over what the different NPC actors might be doing behind the scenes, and book-keeping. If you're a busy person with work, family and a social life, it's a no-brainer: the prep-per-minute to hours-of-enjoyment ratio is hard to beat.
For the final post in the series, I'll list some of the things I use for inspiration when I'm making things up on - either in the planning/setup stage or on the fly during play.