So, you've got your characters, a rough outline of the character arcs and story structure, and maybe an idea of the story title and theme. It's almost time to start writing, but do you know enough about the subject matter to write the story?
Check your outline. You're doing a short story, so you don't really want to spend weeks and weeks on research. To avoid wasting time, come up with specific questions that you need answered. Do you need to research the protagonist's profession? Maybe she does a specific operation that you need to know more about, or if you're writing science fiction, you might need too brush up on how black holes work, for example. Time to hit Google, or maybe the local library. Or, if you're writing about lion tamers and you happen to know somebody who happens to be a lion tamer, go pick their brain, maybe even ask them to read the finished story later if they're willing. (Be sure to follow this up with cake or pie or maybe some movie tickets unless they're your critique partner and you can pay them in kind.)
Sometimes you can't find the info you need. It might be easier to circumvent the problem by changing the story, if the issue is a minor detail. Think about your options, just don't get stuck. If an issue comes up while writing, just make a note and keep going so you don't lose momentum. Much easier to figure out that detail later.
While doing research, pay attention to interesting details and anecdotes. Those help make your story feel more real and unique.
If you're writing a period piece or setting your story in a foreign country, don't forget to research the language stuff. You don't want your 16th century knight to talk like a modern emo kid, now do you?
Museums are pretty great for research, too. Many have informative websites that you can browse even if you can't manage a visit.
And above all, have fun!