The Miracle Worker, a play by William Gibson, is based on the lives of Helen Keller and her lifetime companion, Annie Sullivan.
In terms of conflicts, there are two major kinds: internal and external. There is only one kind of internal conflict and that is man (or woman) against himself (or herself). (This would include having a guilty conscience or talking oneself out of being afraid.) There are several kinds of external conflicts, including man vs. man, man vs. the supernatural (or God), man vs. society, and man vs. nature.
The most prevalent kind of conflict in this play is man vs. man. This would include primarily Annie against Helen, Annie against Captain Keller, the Captain against James, Annie against James, and even the Captain against Kate Keller (but to a lesser degree).
Man vs. nature might be seen in Annie's struggle to keep her eyesight.
Man vs. society can be seen when Annie decides to treat Helen as she sees fit in order to reach through the obstacles of Helen's loss of vision, hearing and speech. The Keller family is very unhappy with Annie's "tough love" approach. Man vs. society is also seen in the behavior of Annie—a young lady from the North—as opposed to the expectations of "genteel" comportment of ladies in southern society in the late 1800s.
The most obvious example of internal conflict is Annie fighting to come to terms with her memories—specifically those of her brother Jimmy, who died when they were very young.
To name a specific instance of man vs. man, perhaps the most memorable incident is in Act Two, scene two, when Annie is trying to get Helen to eat with a spoon and sit nicely at the table. The scene is a memorable one to see, filled with only Annie's commentary, and a great deal of physical acting as Helen and Annie brawl across the dining room table.
There follows the longest and most famous onstage fight in American theatre...
Another entertaining scene (in Act One, scene seven), which involves an early conflict in the play, begins with Annie pitted against Helen, and ends with Annie pitted against the Captain. When Annie will not let Helen have her own way (which the family is accustomed to doing to get any peace), Helen hits Annie in the face with the doll Annie has brought to her (knocking out Annie's tooth); then Helen locks Annie in her room—all on the first day Annie arrives. Helen hides the key, which has a great deal of symbolism in the play, and will be significant at the end of the play. In order to get her out of the room, the Captain must climb to the second floor window and carry Annie down the ladder.
I don't see how I can. There isn't room.
I intend to carry you. Climb onto my shoulder and hold tight.
Oh, no. It's—very chivalrous of you, but I'd really prefer to—
Miss Sullivan, follow directions! I will not have you also tumbling out of our windows...I hope this is not a sample of what we may expect from you. In the way of simplifying the work of looking after Helen.
This conflict, man vs. man, as seen with Captain Keller against Annie, is only one of the many conflicts in the play.