When you analyze any literary work it is important that you are able to identify the main ideas and themes of the work. You should be able to argue what the story is about and how you have interpreted it.
To get a good understanding of the story you should start by identifying the plot---what the story is about. In short stories, this may be more obscure than it would be in a longer work. This is because there is a lower word count and less room to fully form a plot. Nonetheless, this does not mean that a short story cannot have a plot, it may just be smaller and cover less ground.
You should also be able to identify any characters in the story. For short stories, there may only be one, but it is possible to have more. Pay attention to the characteristics of the characters---what they say, what they do, and how they interact with the plot of the story. This will help to shape the meaning and theme of the story.
The setting of the story can play an important role in its overall meaning. The setting can bring context to the overall narrative. In short stories, depending on the story, it may not matter. But it could potentially play a big part in the story and the characters so it is important to pay attention to if it is notable.
Another important part of analyzing short stories is identifying any literary devices that are used. Symbolism may be a common literary device in a short story. You can also look for imagery, similes, metaphors, allusions, and foreshadowing as well as many others. Visit this link through the University Libraries for more information on Literary Devices.
Lastly, being able to identify the theme of a short story is important. The theme is the point of the story the author is trying to get across to the reader. A short story will most likely only have the time to get one theme across, but in longer works, it's not uncommon to have multiple themes. The theme of the story may not be entirely straightforward. To figure out the theme you may need to do a little more investigating into the topics discussed above (University Writing Center, n.d.).