The gift of premonition is the passive ability to receive visions of the past or future. This is Phoebe Halliwell's original power. She later loses her active powers, including her premonitions, for abusing her magic, but goes on to earn it back.
Throughout the series, Phoebe's powers have progressively grown, originally being able to only see the future, to being able to see visions of the past , and then being able astral project into her future self's body, or at least being able to possess a separate body from her future self in a vision. At one point, Phoebe was seemingly able to call for a vision when touching Piper's plane ticket, allowing her to see that Piper was going to miss her plane.
In order to receive a premonition, Phoebe had to make contact with an object that somehow related to the situation or person her vision was about. Several times, Phoebe has receieved a vision without touching anything, one example being when the Seer sent her a vision of Paige's demise, and another being when entering the demon Vinceres' apartment, where the psychic energy was abundant enough that the need to touch anything was absent
The demonic Seer Kira once said that she had to touch objects also when she was starting in her craft. At the time that she made this statement, it was seen that Kira didn't have to touch objects and could seemingly remain lucid in the present while receiving a vision. This could hint at to what Phoebe's powers become should they develop any further.
It is seemingly possible to transfer a premonition to another person, but it seems that the person on the receiving end must also possess the power. Examples of this would be:
-The Seer to Phoebe -Kira to Phoebe -Phoebe to bystander (after Zankou interrupted a power switching spell) -Phoebe to Odin