Experiments have been done to prove or disprove the existence of psychic powers and the paranormal and the results tend to be inconclusive. James Randi, a magician or illusionist, offers a one-million-dollar reward to anyone who can show evidence of psychic powers under observation but this reward has never been awarded to any of the psychics who took up his challenge.
The study of the paranormal is known as parapsychology. In experiments in his laboratory over years, JB Rhine managed to amass a large amount of data in his research into parapsychology and psychic phenomena, but the results tended to be very hit and miss.
Be wary of:
A real psychic should be happy for you to ask some questions before you commit to paying for a sitting or a reading. They should also allow you record the session; this is common practice as it allows you to refer back to it in the future and you can forget details from the reading quite quickly.
Be clear about what you expect from the psychic - he or she may have genuine psychic powers but may not address issues you wanted to address. Different psychics have different specializations - for instance psychic healing is very different from mediumship and so on.
Genuine psychics may have undergone some form of training or be attached to some recognized organization such as the College of Psychic Studies in London. Or if they frequently appear at meetings held by Spiritualist churches, that can be a good indication, as the organization would usually check out a psychic carefully before booking them. However some psychics do just practise from home and don't have any qualifications so you have to rely on your judgement. Word of mouth can be another good way of finding a good psychic.