Learning music by ear is done by repeatedly listening to other musicians and then attempting to recreate what one hears. This is how people learn music in any musical traditions in which there is no complete musical notation. Many people in cultures which do have notation still learn by ear, and ear training is common practice among those who use notation extensively.
In the West learning by ear is associated with traditional and folk music, but many classical music forms throughout the world lack notation, and have therefore been passed from generation to generation by ear.
The Suzuki method of teaching music focuses on playing by ear from a very young age.
See also: Music lesson