She was introduced to acting during the school production of Wizard of Oz. Then while still in school she appeared in numerous television commercials, the sitcom Growing Pains and several television movies. She debuted in the 1988 film License to Drive, which was a teen comedy starring Corey Haim and Corey Feldman. Her strict parents forbade her to appear in the 1989 black comedy Heathers, which had an expletive-rich script.
After high school, Graham enrolled in extension classes of the University of California at Los Angeles (UCLA) and studied English for two years. There she met actor James Woods. They became romantically involved during the time she was cast in the movie Diggstown, where he had landed the starring role. After two years there, Graham withdrew from school at UCLA to pursue acting full time, over her parents' objections. She then moved to Hollywood, where she worked different jobs while continuing to establish herself as an actress.