Start with the eNotes study guide, particularly the Topics for Further Discussion. You'll find some very helpful ideas there.
There are a couple of ways you could approach your study. This play was very controversial when it first appeared on Broadway because of its taboo subject. It is said that when Sam Goldwyn was considering making a movie version, his associate told him, "Forget it, Mr. Goldwyn. It's about lesbians." Goldwyn is said to have responded, "That's ok. We'll make them Americans." When they did make the movie, they changed the love triangle into two women in love with the same man and titled it "These Three."
You might want to center your discussion on that controversial subject and explore how mores have changed or not changed since the play was written. I found an article at brightlights.com that might be helpful.
You might also discuss what is the greater "evil": the perceived homosexuality of the teachers or the lies of Mary--or even the smear campaign that Mary's grandmother carries out on them.
Two movies of the play have been made: "These Three" in the 1930s and "The Children's Hour" in the 1960s. The latter stars Audrey Hepburn and Shirley McClain and is more faithful to Hellman's play. However, my favorite version is the older one because the girl who plays Mary is so much better than the later one.
I hope this helps!
Here's a link below that may provide some helpful information to add to the first answer.
I'd add to the first answer a discussion on the topic of "The Power of a Lie." This is a great topic to discuss with students by the very nature of their present sociology. You can compare and contrast the Mary's lie and it's effects to the student's own experiences with lies, current events' lies, historical lies, etc.
Hope this helps, honestly!