Where does the exposition end and the movement toward the story's climax begin? Where does the resolution stage begin?

Since you haven't provided a piece of literature to analyze I've chosen a very well written and easily understood short story by Gary Soto which is often anthologized in high school literature textbooks. In "The No-Guitar Blues" the reader can easily identify the traditional elements of a short story. 

Edgar Allan Poe was one of the first writers to define and practice the art of the modern short story. Short stories can usually be charted on a diagram which looks similar to a pyramid (see example in link below). The key elements include the conflict which is often one of four types (person vs. person, person vs. nature, person vs. society and person vs. himself or herself), the exposition, which introduces the setting, the situation and the main characters, the rising action, events which propel the plot toward its climax, the climax, the highest point of interest in the story and finally, the resolution (sometimes called the denouement), the point at which the conflict is resolved.

In Soto's story of a Mexican-American boy named Fausto the exposition, which takes up most of the first two pages, tells us that Fausto wants a guitar, yet he has no money and his mother cannot afford such a luxury since the family, while not poor, is not affluent enough to afford everything a child may want. The exposition also tells us that Fausto lives in Fresno, California in a lower middle class neighborhood.

As the exposition suggests, the conflict in the story is simply that Fausto doesn't have enough money for a guitar and sets off into the streets of Fresno to earn money. His travels, which make up the rising action portion of the story, include meeting a dog which, through somewhat nefarious means on Fausto's part, helps him earn $20. The earning of the money makes Fausto feel guilty, which leads the reader from the rising action to the climax. The climax, or highest point of interest, is when Fausto donates the money he earned to the church. Donating the money leaves Fausto with a clear conscience and it is fitting that in the resolution to the story he receives a guitar from his grandfather, thus making his dream come true.

Obviously stories will vary as to when the climax takes place. Sometimes it will be at the very end and sometimes it will be slightly earlier in the story to provide more time for the falling action and the resolution. In some short stories, such as Frank Stockton's "The Lady or the Tiger," we never really get a resolution.