The trial of a former American Broadcasting Co. vice president accused of sexually harassing a female employe opened yesterday in U.S. District Court in Washington as a jury of three men and three women was selected to hear the case that is being closely watched by women's groups and the networks.

ABC is also named as a defendant in the $15 million lawsuit brought by Cecily Coleman, 31, of Arlington. In court papers Coleman charges she was fired from her $60,000 a year job in ABC's Washington bureau after she complained that her boss, James D. Abernathy, 43, then the vice president of corporate affairs, had made repeated unwelcome verbal and physical advances and "told her she could enjoy a promising future 'if she played her cards right.' "

Before her dismissal on May 1, 1984, Coleman, then director of ABC's advisory committee on voter education, a project designed to encourage participation in the 1984 elections, claims that top network executives orchestrated a progam of "retaliation and intimidation" against her after she complained about Abernathy.

Coleman said she learned she had been fired when she received a telegram in Las Vegas where she was attending a convention. When she returned, she said, her office had been "ransacked" and her files confiscated by network officials.

Coleman's attorneys, Mark Lane and Linda Huber, who are being assisted by lawyers from the NOW Legal Defense and Education Fund, claim her treatment was part of a policy of tacit acceptance of harassment by ABC. Sexual harassment or discrimination violates the D.C. code and federal law.

Abernathy, a Manhattan media consultant who left ABC last year for reasons that network officials have said are unrelated to Coleman's allegations, has denied in court papers that he did anything improper. ABC has also denied all charges.

ABC lawyers Stuart M. Gerson and Ronald M. Green, who are defending the network and Abernathy, said in court papers that Coleman exaggerated her credentials on her resume. They contend she repeatedly sought "assistance and advice on matters both professional and private" from Abernathy, that she hung pictures of him in her office and invited him to her wedding at the time the alleged harassment was occurring.

They portrayed Coleman as a consultant to the network who "could no longer hide her failure" to complete certain assignments and was frustrated at not being hired on a permanent basis. The network said Coleman was fired after she had submitted, through her attorneys, a list of eight conditions that ABC found unacceptable.

Among the witnesses who have been subpoenaed in the trial, which is expected to last two weeks, are ABC's Executive Vice President Everett Erlick, James E. Duffy, president of communications for ABC's broadcast group, and Edward Fouhy, former ABC Washington bureau chief who is now an executive producer at NBC.

During jury selection yesterday, Judge Barrington D. Parker questioned prospective jurors about their views on sexual harassment and their membership in or sympathy for organizations, including the National Organization for Women.

Opening arguments in the case are scheduled for Monday and Coleman is likely to be the first witness. CAPTION: Picture, CECILY COLEMAN . . . files $15 million lawsuit