In Hemingway's "Hills Like White Elephants" there is, indeed, much to the dialogue between Jig and her unnamed partner (is not that curious?). Also, symbolism plays a significant role so you may wish to examine the meaning of the railroad tracks that divide Jig and her partner from the other side where the hills are. How does the terrain appear on one side of the tracks as opposed to on the other side?
An examination of theme is also important when one studies such a story. Certainly, Doubt and Ambiguity is a theme as the minimalist style of Hemingway opens the way for this theme. In addition, the author definitely examines the relationship between men and women.
One way to study and examine the elements of stories is to read analyses by professionals. For, critics often provide insights for interpreting and analyzing stories. In libraries there is a collection of criticisms that is entitled Contemporary Literary Criticisms. Look up whatever story you need there and read what professionals write as doing so will enrich your understanding.
I take it this excellent short story is the one that you are having to prepare for. I think generally to study short stories you need to pay particular attention to character and its presentation, how characters change and interact with each other, and how characterisation is revealed in actions, thoughts, dialogue and interactions. Key to this short story is the dialogue. Stylistically, Hemingway choses to step back from the action, allowing the story and Jig and her American to reveal themselves through their conversation. We are left to "fill in the gaps" through our inferences. Exploring how Hemingway does this and what precisely is going on between Jig and her partner would be an excellent place to start.