Research the techniques used by the government of Nazi Germany to oppress people, such as blacks, Jews, homosexuals and Gypsies in the 1930s and 40s, and compare them to the methods the Gileadean government uses to oppress women.
What sort of images would this totalitarian government use to reinforce its control? Design several posters that might be hung in Gilead to remind women of what sort of behavior is expected of them; or write a song that handmaids and Marthas might be required to sing every morning.
The abortion issue has been a continuing controversy in the United States, but it was a particularly important political issue in the mid-1980s, when this novel was published. Read about a prominent figure from that time who was either strongly pro-choice or strongly pro-life. Report on that person's background, what they are doing today, and what you think they would say about the Republic of Gilead.
Find an academic history—similar to the "Historical Notes" at the end of his novel—of the Underground Railroad that was used to free American slaves in the early and mid-1800s. Write a fictional first-person account, based on details from that work, that explains what the experience might have been like for a slave trying to escape.