The details that make up the play's plot arc are described in the summary provided in the links, but one can describe this plot arc in detail by referring to its implications. The basic setting is one that sets up Tillie, a quiet teenage girl, as a protagonist who struggles with the strangeness and volatile environment of her home life. Tillie is interested in science and wants to do well in school. Ruth, her older sister, wants to be popular. Both girls have trouble fitting in because their mother Beatrice is unstable and a social misfit (this is the conflict).
The climax of the play occurs when Ruth gets into an argument with her mother on the night of Tillie's important science fair presentation. Ruth mentions a nickname she heard at school about her mother, Betty the Loon, and Beatrice is visibly shaken and decides not to accompany Tillie to the school, so as not to embarrass her. The denouement occurs when Tillie wins first place and returns home to learn Beatrice has apparently killed their pet rabbit. Ruth has a seizure due to the emotional condition she has suffered since the death of her father. Tillie's final speech is about her experiment growing radioactive marigolds; the theme of her project is that radioactive contamination produces mutations, and it is understood (in a way that makes this a moment of resolution, to some extent) that this side of contamination refers to her own toxic home environment and the effects of mental illness on her own life.