Better known as palm-reading, this is the study of the lines on the hand to foretell the future. According to The Book of Divination by Ann Fiery the dominant hand is the one read, as the non-dominant hand will reveal more about the subject's past than future. How to read the palm is too long to go into in a post, but Fiery devotes a whole chapter to it, and the information can probably also be found on the internet.
Although the modern stereotype is of the "gypsy fortune teller" at a fair somewhere, chiromancy is said to date back to ancient times. According to Wikipedia, it is said to have its roots in Hindu Astrology, from where it made its way across the ancient world.
The more detailed analysis of the whole hand, taking in the shape of the hand, fingers, and fingernails, is known as Chirognomy, not to be mistaken for chironomy which is a method of conducting vocal music performances.