In order to conquer Earth he deceived a depressed young woman named Arella who joined a cult that was trying to kill him. He took the form of a hunky young man and married her. By the time she learned of his evil nature, she was pregnant with Raven and abandoned by Trigon rather than forced into being his queen. When Raven was born she was taught to control her emotions to fight her father's evil influence. He may have some love for his daughter, hinted when he spared the Earth in exchange for Raven going with him (he broke his promise and tried to conquer Earth anyways), but mostly sees her as just a servant and pawn.
He is the main antagonist of the Terror of Trigon arc in the Teen Titans comics where was finally destroyed when Raven's corpse channeled the energy of Azeroth's souls that erased him from existence in a purifying light, though his followers led by Brother Blood have sought to revive him. He was also the main antagonist of the fourth season the animated series Teen Titans, where Raven's confidence and hatred for him gives her the strength to kill him. And he was the main antagonist of the DC animated movie, Justice League Vs. Teen Titans, where he was sealed away in the shard of a magic jewel.
He also appears as a recurring character in Teen Titans Go! as a stereotypical sitcom dad. Unlike other versions of himself, this version actually loves his daughter and wants her to become evil like him and thus is the ONLY version of Trigon that is isn't pure evil.