I ran a mystery just today (well, the second half of the mystery that started last week). Here's how it played out... There are (sort of) some spoilers for the first Dawn of Defiance module in here, though I am not running that module.
One of the characters owed money to a crime lord, so he went to make his payment. Simple and straightforward. No mystery there. I'm getting to it.
While the characters were having their meeting with the crime lord (I used the droid Switch, gaffled out of the Dawn of Defiance campaign), he asked for a favor, which would eat up some of the character's debt. A friend of his on another space station had been kidnapped. The crime lord wanted the friend extracted and brought back, so that an eye could be kept on him. This is the mystery. The characters need to discover the identity of the kidnapper and the whereabouts of the kidnappee, so that they can do their stuff.
During the meeting, Switch's rival Ganga Lor bursts in, demanding that Switch hand over his share of the bounty. As it turns out, the characters have a bounty on their heads, and Switch used this fact as a way to draw Ganga Lor out into an open conflict, in the hopes that the characters would kill him. Battle ensued. Both Ganga Lor and Switch ended up fleeing from the fight. The characters took this opportunity to do some investigating. They didn't find a whole lot about Switch's operations (which is what the devious fiends were looking for) but they did find out about an asset of Switch's on the station on which the kidnapping had taken place.
Although they were unsure of whether or not they should actually be helping out this crime lord (whom they discovered had totally set them up as a cat's paw), they decided that they should at least go and get this guy unkidnapped, since it was the right thing to do (and also, since it was the adventure that I had prepared for them at the time). So... Off they went to Tansarii Point station.
Arriving at the station, they went straight to the contact, Lenny the Sleezebag. Lenny the Sleezebag believed that agents of the Black Sun were responsible for the kidnapping, since they were engaged in some heavy duty shenanigans on the station recently, and this fell pretty much right into their MO. Now, I had expected the players to check out the scene of the crime, which would have provided them with some additional clues, pointing them to a Black Sun hangout. They did not. Instead, they headed straight for some Black Sun mooks and started wailing on them, with questions. This was fine by me. not only did it allow the players to get out some of their aggressions, but it still furthered their goals. Also, it really riled the Black Sun up, so that there was going to be a reckoning.
All this beating up of mooks led the characters to the previously mentioned Black Sun hangout. Predictably, a battle ensued (though the character that owed money to Switch did try to sell him out to the underboss, which didn't really pan out). The characters were (more or less) victorious and, though they did not locate the kidnapped engineer that they were looking for, they did find another clue to his whereabouts. Following this clue led the characters to a starship battle, which yielded them their kidnap victim, and also a starship that was only moderately destroyed.
In the end, the characters decided to return the engineer to Switch, because the reward was just too valuable to pass up, and because they couldn't convince anyone else (besides Ganga Lor, who informed on them to the empire just as soon as he got a chance) to kill the conniving droid.
There were a couple of mini-mysteries in this adventure, as well... None of them were necessary to completing the adventure, but were just an extra bonus for the players. The first was that Switch was attempting to use them to do his dirty work (i.e. trying to kill off his rival). The second tied back to their previous adventure. They thwarted the empire and got an inquisitor interested in them (thus the bounty on their head). The inquisitor was using the force power Far Seeing to track them down, which was giving the force sensitives the willies. They found out that the Inquisitor was chasing them, and knew that the crime lord Ganga Lor had told him where they were heading, but they did not put together that the inquisitor followed them to the original station before there was any informing. I am going to continue to have the inquisitor show up where they are (or just were) until either they figure it out and deal with him, or until something really bad happens because of it (like, the inquisitor discovers the whereabout of the rest of the rebels that they hang out with).
In the previous adventure, there was also a side mystery that they failed to solve. There was a traitor (whom they are calling Darth Informant) that they failed to identify. It should lead to some more interesting adventures down the line, I hope.
Hopefully, this will help to illustrate how I think mysteries work best (and also more or less follows the action leads to clue leads to action bit from previous posts).