To make a long story short, all of them.
Various properties of starts can be studied by measuring the frequencies and corresponding intensities of electromagnetic radiation from a star. Assuming a star is not moving with respect to the Earth (or, put more simply, is moving as fast as the Earth is and in the same direction), the intensities of the wavelengths emitted by the star can be seen from Earth as having a bell curve distribution whose peak corresponds with the star's temperature.
However, this bell curve distribution is not perfect. At several specific frequencies, the intensity of emitted light is greatly decreased. The frequencies influenced by this effect and the degree that this effect occurs are dependent on the component elements and corresponding concentrations of these elements. Therefore, by analyzing the frequencies that are "missing" from the electromagnetic spectrum, one can derive the chemical composition of the star.
If the star is moving with respect to the Earth, this distribution of light is distorted even more. As a consequence of relativistic physics, the wavelengths of light emitted from the star will appear to have a higher frequency as seen from the Earth than what was emitted if the star is moving toward the Earth (this is called "blue shift", as visible colors appear more blue). Conversely, the Earth will see lower frequencies of light than were originally emitted if the star is moving away from the Earth (this is called "red shift", as visible colors appear more red). However, since the distribution of light emitted from the star has "missing" frequencies, and since the original emitted frequencies are known for these "missing" frequencies (as they correspond with the frequencies emitted by known compounds), the entire distribution of light can be shifted back to its rightful place. Moreover, the amount of this shift is dependent of the relative speed between the Earth and the star; therefore, the star's speed can be determined from the star's light as well.
telescopes
An HR gram
A prism can be used... but there are probably other ways.
Telescopes
The study of the stars is astronomy.
Spectroscope
Why did Asians study stars
Fresnel's biprism is commonly used in experiments to study interference and diffraction of light. It can be used to produce interference fringes, measure the wavelength of light, and study wavefront properties. Additionally, it is used in optical systems for generating coherent light sources.
Arecibo
People in the past usually studied the stars because they used it to make Calenders and days
The proper name for the study of stars is astronomy. A person who studies stars is an astronomer.
An observatory is a location used for observing terrestrial and/or celestial events