Don’t do this. No, don’t you ever improvise an adventure. Players will notice and hate you… But if you really, really have no choice. This is a sequence you may use, while you ask your players a few minutes to “review your notes”
1. Steal a plot
Start searching your own memory first; look for any action, scifi or mystery film. It does not have to be of the same genre of your campaign or game. You could take Star Wars and make it into a Fantasy story, you only need to adjust a few things:
- X-Wings and Ties could be horses or some other noble stead
- Big space ships could be galleons or even armies
- Planets could be “kingdoms”
- And the planet killer death star might be a sinister fortress, its weapons including some Armageddon grade monster swarm, unstoppable once it’s launched, but that it requires weeks of dark rituals.
2. Discover the critical elements.
Let’s suppose you are going to do the fantasy Star Wars thing. The critical elements you need to get the game going would be:
a) Discover the initial scene
I’d start with the meeting at the Tatooine Inn. That’s easy to set up in a fantasy game, a bit typical, but it still works. Then I need I need some bounty hunters, and some storm-troopers. These are easily translated into fantasy npc, perhaps you could easily use stock npcs if your game provides any.
b) Discover the Big Bad Guys
Star Wars, who could they be? 
The Emperor could be a high level wizard and Vader a medium to high lever Wizard/Warrior
c) Note the main locations and translate them into your genre
The Inn in Tatooine, an inn; the Ewok forest, a forest; space could be the sea; Coruscant a city; the cloud city, an isolated citadel in the mountains or a floating city perhaps?
d) Translate the stuff they use
Light sabers? a Magic Sword, Blasters? Bows, Armor… armor, duh. Just do not try to mimic everything; there’s no time for that if you are improvising. Simply use whatever STANDARD item of your game seems closer to what they used, and keep moving.
End of Part I.
On part II, I’ll share a few tools to build a huge world on this basic elements, and fast.