I'm going to lay out a simple technical plot as an example. This one will be science fiction.
Preventing a Supernova
For our first one, let's presume that our system is Stars Without Number, and the party is composed of four characters (a scientist, an engineer, a psion who's also the face and a soldier who's also the pilot) who are part of the scout service of a TL4 starfaring society. They're zipping around when they get a transmission from Scout Central telling them to head to System X and deal with the situation there.
The briefing they receive is where you, the referee, present the problem they're going to be dealing with. In this case, the problem is that a red giant star with some alien ruins on one of its orbiting planets is unexpectedly going to turn into a supernova much faster than expected. This was detected because some strange signals from above the plane of the ecliptic drew the attention of a stellar observatory at Scout Central. Scout Central wants the supernova stopped because the explosion endangers a neighbouring star system.
The elements of the problem are:
1) The red giant star
2) The alien ruins
3) The strange signals
The PCs drill over to System X, and are given the choice of which one of these they want to examine first. At this point in time, the effects of the red giant's incipient explosion are minimal, but they don't have much time before it blows. Maybe you provide a diegetic timeline (72 hours!), maybe you don't (it's looming but unpredictable), whichever suits your preferred style.
The PCs decide to investigate the star first. Investigating the star involves a few challenges. They need to get close enough that the heat of the star will affect them, and they'll expend some of their limited time jetting around the star.
The PCs successfully zip around the star scanning it while dodging solar flares. From this, they learn that the star is giving off more energy than it should for its mass, and is much more unstable than it should be. At the end of their examination, two things happen. First, the star's energy flares, making sensors and communications much more difficult (the first effect kicks in). Second, the PCs hold a meeting onboard their ship where they decide what to do based on what they know. The scientist and engineer roll their skills, and they discover that based on what they know and have available, their only option is to drill through the star using their FTL drive, and bleed the energy off into other dimensions as they do so.
This apparatus has some pretty obvious flaws:
1) The death of everyone aboard the spaceship even if it works properly
2) Need to get into the corona of the star in the first place to work
3) One chance to succeed
So the PCs decide not to do this, and instead examine some other element of the problem to see if they can get further insight and come up with a better solution. They decide they don't want to land the starship just yet, so they go to check out the strange signals. So they fly over to check it out.
The strange signals turn out to be coming from a giant space whale-type thing. It's hanging around above the star. The PCs have to get close without attracting the space whale's attention, because it's firing a giant beam periodically out of its eyes into the sun and slurping up helium. Because this is a technical plot, not a bug hunt, the PCs can get some readings that tell them that the space whale is basically a giant fusion reactor in space whale form and blowing it up would make a mininova.
So the PCs do some submariner-in-space silent-running maneuver, and get to observe the whale as it feeds. Since the apparatus they came up with last time sucked, they decide to use this opportunity to conceive a new one. Everyone gets together and rolls some skills. The outcome is that they think if they can get the space whale to reverse what it's doing, they'll be able to prevent the supernova. The apparatus they conceive of is to configure the spike drive so it lenses the psion's mind control powers, allowing them to get control of the space whale's brain.
The initial flaws are:
1) Neither their spike drive on its own, nor their psion, has enough power to give this a good chance of working.
2) What does "reverse what it's doing" even mean once they do get control?
3) This will draw the space whale's attention, and could provoke an attack.
In this case, because they've already examined the star, you're generous and you let them cross out flaw #2. The scientist and engineer can figure out what the whale's doing based on what it's done to the star, and can cobble together a crude approximation of what unzapping the sun means.
As the PCs are figuring this out, the space whale zaps the star once more, and suddenly the stellar surface starts roiling and shooting out waves of cosmic rays at levels so intense the PCs' starship has to retreat or else everyone will get radiation fried. This is the second effect, triggered by the PCs examining the space whale. In this case, not only does this mean that the PCs risk incineration by cosmic rays periodically, they also might not be able to get close enough to the whale to use the apparatus as it stands. Rather than treat this as a new flaw (though I guess you could), it seems simpler to just wrap this into flaw #1 - not enough juice - with the increased distance they need to do this from simply making that worse.
So, to put some distance between them and maybe figure out how to get rid of another flaw, they decide to check out the alien ruins on X Prime. They get down there, and a ton of weird stuff happens as they dungeoncrawl through a ruined alien city. Eventually, they discover the source of most of the weird stuff is that there's one ancient alien hermit who's the last survivor of his people and who's super psionic. He's holed up in the ancient space telescope that still works, and he's super lonely. He probably called the creature in the first place accidentally as he projected his mind out into the cosmos via the space telescope, but he can't stop the whale from destroying the star, and thus killing him.
The PCs talk it over with him, and make some skill rolls as they examine the ancient space telescope and talk to the gelatinous worm-swarm who's so lonely. They get some successes, and he agrees to help, teaming up with their psion, showing her how the space telescope works. The scientist and engineer rig it up to the starship for extra boost, and the end result of all of this is that flaw #1 goes away. Unfortunately, during the time they spend doing this, they also register the space whale continuing to fire. Now the very surface of the star is roiling, and sending deadly waves of cosmic radiation pulsing down onto the surface of the planet. The PCs are going to start taking damage every 1d4 rounds. They rush into their space suits and get the worm-swarm into a mylar blanket or whatever, to buy them a few extra rounds each time (you shift the damage interval to every 1d8 rounds).
So now, the PCs' main risk is that doing this is going to draw the space whale's attention, and it'll take a bit of time between turning the device on, aiming, using the power, and then getting the whale to fire. This is the activation phase of their apparatus. You run this as an action sequence, lots of tension. They can make multiple attempts, but maybe the whale starts firing after the first failure, and someone nearly gets burnt to death by cosmic rays but is saved when someone else does something risky, and like, the ancient space telescope building is crumbling and all that jazz. Eventually the PCs win, and get the whale to zap off enough helium (or whatever) that the star stabilises.
Mission accomplished. Number of bad dudes shot to solve this problem: 0. The PCs now have the last survivor of a gelatinous worm-swarm civilisation as their bud, and they take him off to land on the space whale, who he infests the intestines of, and they fly off into the black together, firing goodbye laser blasts of friendship.
I plotted this out over my lunch break today simply by taking the model and making sure I'd filled out each section of it. The amount of scientific research I had to do involved checking Wikipedia twice to make sure a supernova is what I thought it is (yes) and to make sure red giant stars still had helium (yes, mostly on their surface, vs. younger stars where it's more buried). Almost all other "science" in this adventure is pure technobabble, but it's meant to fit together to motivate decisions and actions by the PCs, rather than to provide a cohesive and accurate summary of stellar lifecycles. I came up with effects each time by knowing that I wanted the star stuff to get worse, and just picking which possible option based on what these (fake) PCs had done.
Anyhow, I hope this example provides a useful illustration of how to apply the model to actual games.