Many of the techniques used to study exoplanets rely on spectroscopy: the study of light emitted by stars and other hot bodies by measuring the distribution of light intensity as a function of wavelength or frequency. The full distribution of light is called the electromagnetic spectrum, which extends from the low frequency and long-wavelength radio waves, to the high frequency and short-wavelength gamma radiation (as seen in the image below).
Like the Sun, stars emit at wavelengths across the electromagnetic spectrum, with many discrete absorption lines at certain wavelengths. Absorption lines are 'breaks' in a spectrum (shown in the image below), due to a deficiency of observed photons, or light particles. This occurs when photons interact with atoms or molecules, which can absorb light only at specific frequencies.
The light emitted by a star or planet contains unique absorption lines due to the elements and molecules present in the star, or in the planet's atmosphere. Telescopes can capture this light and redirect it into a spectrograph (which could be a spectrometer, spectrophotometer or spectroscope) or a photometer. These scientific instruments can be used to measure and study light by splitting it up into its constituent frequencies. Using this and other basic techniques, astronomers can infer a planet's mass, temperature, brightness and atmospheric composition.