Posture and style
Perhaps one of the most obvious things one needs to know about playing an instrument is how to hold it, or sit at it. For many instruments, the best way to move the fingers to achieve a desired effect may not be at all obvious. For example, when playing the piano, "fingering" — that is, which fingers to put on which keys — is a skill slowly learnt as the student advances, and there are many standard techniques which a teacher can pass on. In addition to fingering, a guitar player learns how to strum, pluck, etc; players of wind instruments learn about breath control and embouchure, and singers learn how to make the most of their vocal cords without hurting them.
Theory
In order to more fully understand the music being played, the student must learn about the underlying music theory. Along with reading musical notation, students learn rhythmic techniques like controlling tempo and recognizing time signatures, as well as the theory of harmony, including chordss and key signatures.
In addition to basic theory, a good teacher will stress musicality, or how to make the music sound good. This includes tone, phrasing, and proper use of dynamics.
Drilling
Although not universally accepted, many teachers drill students with the repetitive playing of certain patterns, such as scales, arpeggios, and rhythms. In addition, there are flexiblity studies, which make it physically easier to play the instrument. There are sets of exercises for piano designed to stretch the connection between fourth and fifth fingers, making them more independent. Brass players practice lip slurs, which are unarticulated changes in embouchure between partials.
Pieces
Finally, the teacher will give the student a set of pieces of slowly increasing difficulty. Besides using pieces as an aid to teaching various elements of playing style, a teacher will also confer more esoteric concepts such as expression. Pieces are undeniably more enjoyable than theory or scales, and an emphasis on pieces is usually required to maintain motivation.