I didn't know anything about this station before I started - nothing about the people who live there, who work there, nor who runs the station. I don't know anything about the Alien situation nor do I know anything about the technology level. All I know is that it's a space station. Luckily for me, there is a free Play Set for Fiasco called Freeport 2717 that supports this exact situation.
So, back to the story. I had my three characters and I had a bunch of random numbers, so I start with establishing the relationship between my characters.
For the relationship between Character A and B, I picked a sexy one. Crime. They have some sort of criminal relationship. Between B and C I checked my dice and picked out "Community", they're both involved in some sort of community together. Then for the relationship between C and A, I picked "Work". After determining the bigger picture, and having used up three of my dice, I looked at the pile to see what was left. Some sixes and ones, and then one of each of the remaining numbers. Hmm.. A quick glance at the Crime-relationship, and I picked out Assassin/Client as the more specific relationship. Interesting. Moving on, the community relationship was specified as "Elected Official" and the final relationship, the one between Character A and C, was defined as "Doctor/Patient". So I already have an interesting mixture to work with here.
Character A is an assassin of some sort, who has an elected official as client. Character B, an elected official of some sort, together with Character C, a doctor, who in turn has Character A as a patient at some part in the story.
I was now left with half my dice - six random numbers and all of a sudden my options were running out.
Moving on to needs, I decided that my assassin needed to leave the station somehow. That's his driving force in this particular story, so I picked one of my remaining "ones" among the dice. At this point I went straight for the more detailed description of having to leave, and picked number five, "because two contracts on my life is more than enough".
This is where the story truly started to form in my mind. Here we have an assassin with a contract on his head (and not just one, two in fact), but why? That's a story in itself. My mind immediately said, he received a contract to kill himself and the client is the "elected official". I'm imagining that the assassin is actually working with two identities, one he's an assassin, akin to Superman, and another one he's a "Clark Kent". Is it perhaps possible that he's on the same council as the elected official, on opposing political sides, and his assassin alter ego receives the contract to kill "the real him"?
Basically, my mind was racing at this point and that's simply from following the guidelines of establishing relationships. I won't go into further detail here, but I hope you can see how not only does Fiasco help with coming up with plot ideas, the game also helps with constructing interesting characters!
I'm sold. :)