To be psychic simply means being able to obtain information in other ways than through using the physical senses of sight, hearing, etc. Clairvoyance is probably the best known and most commonly used psychic sense, and is often given as the name for all psychic abilities. Clairvoyance means "clear seeing", not with the physical sight, but with the inner, spiritual sight; it is a natural ability, just as normal eyesight is.
Clairaudience means "clear hearing", when you can actually hear the voices of people that are not physically present.
Telepathy is the transmitting and receiving of thoughts. With telepathy, it is possible to communicate with people who speak other languages, for the thoughts are transmitted free of language, and are automatically translated by the recipient.
Channelling is when you allow a trustworthy spirit being to speak or write through you while you are in a trance.
Psychometry means holding an object, and picking up impressions from it, usually clairvoyant images. Intuition, or direct knowing, is having the feeling, or a strong impression of some information without pictures or sounds.
There is another psychic ability which is very common, and very much a mixed blessing. A sensitive will pick up and feel in their own mind and body, the feelings of another person. This is great if the other person is well and happy, but can be very uncomfortable if they are sad or ill.