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The origin goes to Newton's analysis of light passing through a glass prism.

There are many claims as of who invented the spectroscope, but the earliest reference is in 1814, when Joseph von Fraunhofer discovered dark lines in the color spectrum of the Sun (the lines are still called Fraunhofer lines)

In 1850-1860, the instrument was perfected by David Alter, Anders Jonas Ångström, Gustav Kirchhoff and Robert Bunsen, which sometimes are credited with its invention.

The basis is the fact that light of different colours is transmitted through a prism (or reflected by a grating) at different angles. A slit is used, to ensure that each color forms only a narrow image at output, so you can have a sharp image of the succession of colors (so they won't overlap).

You can check any encyclopedia on thesubject of spectral analysis; the final part is the Kirkhoff laws of spectrometry:

1. A hot solid object produces light with a continuous spectrum (filament of incandescent light bulb)

2. A hot gas produces light with spectral lines at discrete wavelengths (fluorescent bulb; these also have a layer of phosphorus-like substance, absorbing the ultraviolet spectrum and converting it in visible light; the lines produced by this emission are wider than those of the gas)

3. A hot solid object surrounded by a cool gas (i.e. cooler than the hot object) produces light with an almost continuous spectrum which has gaps at discrete wavelengths depending on the energy levels of the atoms in the gas. This is the case of the Sun.