How would I write a research paper about "The Lottery" by Shirley Jackson?

If you are asked to write a research paper on a topic, your instructor wishes you to examine what other people have had to say about a topic. A research paper is an invitation to find out more about a subject.
Since you are working on "The Lottery," you could go in several different research directions. One would be to research what scholars and critics have said about the short story. What have they praised it for, and what have they found not to like about it? Have reactions to the story changed over time? The story, for example, became very popular during the Vietnam war, when the government instituted a draft lottery and people saw a parallel. That could be an interesting angle to research.
You could also do some biographical research into Shirley Jackson, such as why she wrote the story and how she reacted to its success.
Another research angle would be to actually look at societies that performed human sacrifice to help with the harvest. You might, for example, want to read more about the Pawnees and the chief who ended child sacrifice.
The best way into research is to think about what unanswered questions the story leaves you with. How can you find answers? Also, what personally interested you most about the story? Can you find out more about that topic?