Most people have this already if they have abnormal subconscious and psychological issues, but without any mental concentration or vividness of the mind, one rarely gets it. Those who are true full psychics or half psychics can cause them to happen more often.
Premonition is mostly dream-based (you can have them when you are awake too, but daydreaming at the same time.) and one does or cannot control them.
Unless you constantly meditate every day and know how to do so correctly of course, otherwise any parapsychological ESP like precognition and premonition are by accident in most normal humans.
People seldom remember dreams, they will not remember having the premonition or precognition unless they have an epiphany later on and remember having it at that moment.
Precognition and Premonition are examples. When he has bad dreams or nightmares, he has premonitions of villains that he has not personally seen yet.
When he has good dreams, he has precognition of the future, able to know what is going on without having to be personally there. This was proven when he was bed ridden with the Heart Virus and he claimed to know what was happening even if he wasn't conscious half the time.
He had a nightmare of two Saiyans (Nappa and Vegeta) attacking his wife and son in a filler episode, it was a premonition. That's how he was able to know what they looked like people!
Gohan, (Goku's Son) had a premonition of Cell in a nightmare, the one who bitchslapped Chi-Chi to death and stepped on her neck and one-shots Piccolo and steps on his head.
Odd from the french anime: Code Lyoko, has precognition and premonitions often in the first season, most of the time it was Aelita, Yumi or Ulrich in danger.