What is the chemical composition of the Sun? How do astronomers identify the types of elements it contains?

Sun
The flaming gaseous mass of the Sun contains many of the chemical elements present on the Earth. When a ray of sunlight is analyzed by a spectroscope and split up into its colors to form a spectrum, the bands of color seen denote the elements present in the Sun. Each chemical element when heated to incandescence emits light of a particular wavelength, producing a characteristic color in the spectrum. Though some wavelengths are absorbed by the gasses in the Sun’s envelope or in the atmosphere, they nevertheless leave dark absorption lines in the spectrum, and their presence can be discovered.
The Sun, like most other stars, is made up mostly of atoms of the chemical element hydrogen. The second most plentiful element in the Sun is helium, and almost all the remaining matter consists of atoms of seven other elements. For every 1 million atoms of hydrogen in the entire Sun, there are 98,000 atoms of helium, 850 atoms of oxygen, 360 atoms of carbon, 120 of neon, 110 of nitrogen, 40 of magnesium, 35 of iron and 35 atoms of silicon. So, about 94 percent of the atoms are hydrogen.

Additional reading:
Sun (Wikipedia)

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