Due to limits in length, below are a few ideas to help get you started. To write a summary, you first want to break the literary work up into sections. Dealing in sections helps you see exactly what's important as a main idea and what isn't. Since F. Scott Fitzgerald has already broken up the short story "Winter Dreams" into six episodes for you, your workload for summarizing each episode is much easier. Next, all you have to do is figure out which event/events are most important in each episode.
To figure out what's important, all you have to think about are the elements of the story, especially the plot. Think about the story's resolution, which is how the story ends, and the climax, which is the most pivotal moment in the story, the moment that leads to the resolution. Also, think about the characters, especially the protagonist Dexter Green. Think about what he is like as a character, what his driving motivations are, what things he wants to achieve.
Looking at all of the above will help you be able to pick out what's important in each episode. As an example, in the first episode, we learn that Dexter has a fairly decent job working as a caddy at a golf club that caters to the wealthy; he is even highly valued as a caddy. However, we also learn that, by the end of the episode, Dexter decides to quit his job as a caddy. Why does he decide to quit? He has found himself falling in love with a wealthy 11-year-old golf club member and did not feel comfortable working for her as a caddy. Hence, he quits his job because, developing feelings for her was such an emotional shock, he felt he needed to do something equally shocking:
The enormity of his decision [to quit] frightened him. He was a favorite caddy, and the thirty dollar a month he earned through the summer were not to be made elsewhere around the lake. But he had received a strong emotional shock, and his perturbation required a violent and immediate outlet.
Hence, it's evident that developing feelings for the young girl and quitting his job are two main events worth summarizing.