Characterization is the means an author uses to describe or develop a character for the reader. The brevity of a short story insures that there will be few characters. The main character is the only character who is really developed, so characterization in a short story is fairly easy to analyze.
Name the main character. Sometimes in a short story, the main character will be the only character. Other times there will be a few characters but only one who is mentioned repeatedly throughout the story. Your analysis of characterization needs to focus on the main character.
List the main character's physical attributes. As you read the story, keep a running list of any physical descriptions of the main character. The author may reveal the character's height, age, hair color, style of dress or other things about his appearance. Since the story is short, the author won't have time to describe everything about the main character. Therefore, the details he does reveal are important and will probably give you clues about the character. For example, if the main character is described as having a sinister smile, the writer is not only using alliteration to color his writing, he is pointing out that there is something evil about the character.
Identify character traits the main character displays. An author can reveal character traits in a description of the character's appearance or in how he acts and what other characters in the story say about him. Characterization in a short story is usually somewhat one-dimensional. The main character may be evil, unpleasant and unhappy or helpful, caring and giving. She won't usually display contradicting qualities.
Consider the source of your information when deciding how accurate it is. What another character says about the main character may be more reliable than what he says about himself.
Notice how you learned about the main character. Writers have different ways of describing a character in a short story. They can use narration to describe the character, dialogue to reveal her attributes, or some combination of techniques.