You should write just as much as necessary, and nothing more.
Short stories are supposed to be like that - short. Even if it's a fantasy setting, maybe a wildly elaborate one, you should not describe more than you need to bring the short story to an effective, satisfying end.
Any information you give should serve at least one of those purposes:
- Allow the reader to understand what happens, or
- emphasize something about the theme of the short story.
Point one basically means that you can't pull important informations on the setting without having them introduced, first.
Let's suppose you're writing a short story about a warrior exploring an unknown dungeon. He stumbles on a chest and tries to open it, expecting to find some treasures, but - surprise surprise - there's a magic trap inside and he bursts into flames. While that would be quite a big shock for the audience, it wouldn't be satisfying if you have not hinted at the existance of magic in the world.
In other words, all the elements that come to play in your short-story arc should be somewhat understandable to the reader.
Point two is about something more subtle. Let's say that the underlying theme of your short story is greed or proto-capitalism in your fantasy setting. Then maybe it would be interesting to talk about the guild system in your world, the trade routes, the kingdom's taxes, the slave-runned gold mines ... you name it.
Maybe those things don't come into play into the plot per se, but they add relevant flavour. A character may just stop and think:
The elf had a thick layer of sweat on his brow, like a slave after a long day mining gold for silk-gloved hands.
Ask yourself: what's the point of my story? What is the theme?
Remember: you don't have to "explain" everything. Most of the times, hinting at something is enough - the audience is smart and will connect the dots. You don't have to stop and tell how everything works, everytime.
What you want to avoid at all costs is useless exposition. You may feel the temptation to show the readers how cool your worldbuilding is: try to resiste the urge. No one cares if you've got the most fantastic magic system in your story if it doesn't come to play, or it doesn't help making a point.