A physical description is usually the reader's first introduction to a character, and can provide important information such as the character's age, fitness level, grooming and socioeconomic status -- although other elements may later undermine this first impression.
The manner and content of a character's speech also shows the reader who that character is. A character's speech may tell the reader something about the character's education level, geographical location and attitudes. Examples for writers who used this element to great effect include Mark Twain, William Faulkner and Nelson Algren, among others.
The character's psychology is, perhaps, the most important of all character elements. This is where the meat of characterization exists and what separates fully-developed characters from flat, boring stereotypes. Psychological traits embody a number of aspects that make up a whole person, among them thoughts, feelings, habits and world view. These traits are what dictate the decisions the character will make in the story.
Short stories are about people making decisions, accomplishing or failing to accomplish goals in an effort to overcome an obstacle. A character's actions are what moves the narrative forward, creating and resolving conflicts, and establishing a short story's sequence of events and rhythm.
In addition to a character's own physical and psychological traits and actions, we also learn about a character through the reaction of other characters. In some cases, these reactions are the compelling factor in causing a character to change. For example, in Charles Dickens' story "A Christmas Carol," not only does the reader gain much insight into Scrooge's character through the reaction of other characters, Scrooge is ultimately transformed after seeing himself through the eyes of others.