How are the instruments in an orchestra grouped?

There are multiple classifications.

Ancient System

Stringed Instruments - Instruments played with strings.

Percussion Instruments - Played by beating/hitting/shaking the instrument.

Woodwind Instruments - Played by blowing and wrought from wood.

Brass Wind Instruments - Played by blowing and wrought from brass.

Sachs - Hornbostel

Chordophones - Played using strings.

Membranophones - Percussion instruments previously made with animal skin.

Idiophones - Played by the use of its body.

Aerophones - Played by the use of wind.

Schaeffner

Instruments with solid, vibrating bodies.

Instruments with air.

Range

Soprano

Alto

Tenor

Baritone

Bass

Contrabass