A poet's reading is rudely interrupted by a woman's cellphone ringing. Sorry, that was actually a beeper. Oh, man, we just realized that this movie's future gets destroyed before Spotify, Amazon, and Netflix.
Those poor people.
The woman turns out to be a psychiatrist, one Dr. Kathryn Railly. She goes to the police department, where a detective describes to her a mentally unstable man who took on five cops earlier that day.
The man is revealed to be—you guess it!—James Cole. He's found himself in another prison cell, bloodied and chained to the floor. Jury is still out as to whether this is an improvement from his previous situation.
Cole explains to Railly that he needs to go and gather information. She asks him what year he thinks it is, and he says 1996.
She informs him that 1996 is the future. It's 1990.