The case was brought after an article by Heard in which she claimed to be a victim of domestic abuse.
But Ms Heard's team argued Mr Depp brought her to court simply to "destroy her".
Mr Depp, 58, has denied any abuse and has sued his ex-wife for $50m (£38m).
Ms Heard has in turn, sued him, with a $100m counterclaim.
Hordes of fans have already gathered outside the Virginia court for the trial, expected to last up to seven weeks.
At issue in the trial is Ms Heard's 2018 opinion piece in the Washington Post, describing herself as a "public figure representing domestic abuse". Mr Depp says the article - which does not mention him by name - is defamatory and derailed his career.
Beginning a day of opening arguments, Camille Vasquez, a lawyer for Mr Depp, told jurors Ms Heard had been the aggressor throughout the relationship.
Ms Heard concocted a role for herself as victim, Ms Vasquez said, once Mr Depp had asked her for a divorce in attempt to "avoid humiliation".
"She is obsessed with her public image," she said. "She has been living and breathing this role for years now and she is preparing to give the performance of her life."
Lawyers for Ms Heard instead claimed the actress had endured emotional, verbal and physical harassment at the hands of Mr Depp.
Mr Depp wants to "haunt her, to wreck her career", attorney Ben Rottenborn said.
Christi Dembrowski, Mr Depp's older sister, was first on the witness stand. Responding to questions from Mr Depp's lawyer, Ms Dembrowski described a volatile childhood, shaped by their mother's abuse.
"Mom would, she would scream, she would yell. She would hit [Dad], call him names," Ms Dembrowski said. Mr Depp never fought back, she said.
Ms Dembrowski described her famous sibling as a gentle and loving brother, son and father to his two children.
According to Ms Dembrowski, her brother's demeanour changed when he became involved with Ms Heard. "He seemed sadder," she said.
Ms Heard would often insult Mr Depp, Ms Dembrowski said, recalling an instance when Dior wanted to hire Mr Depp for an advertisement campaign.
"She [Ms Heard] said, 'Dior, why would Dior want to do business with you? You don't have style... She called him an old fat man," Ms Dembrowski said.
Mr Depp's sister told jurors she was "devastated" by the news that Mr Depp would marry Ms Heard, and fearful that her brother's relationship was mirroring that of their parents.
"If I'm honest, I debated going [to the wedding]," she said. "I wanted to make sure that I showed up anyway, because I wanted to make sure, honestly, that my little brother knew I was going to be there no matter what."
Ms Dembrowski is the first of an estimated 120 witnesses who will be called to testify in Virginia in the coming weeks, helping to sketch competing accounts of Mr Depp and Ms Heard's relationship.
On Sunday, ahead of the trial, Ms Heard released a statement to Instagram, writing that she has "always maintained a love for Johnny".
"It brings me great pain to have to live out the details of our past life together in front of the world," she said.