They tries to understand the universe, how planets, stars and galaxies are formed; analyzes the light of variable stars or quasars; searches for planets outside the solar system or black holes in the heart of galaxies; studies the spectrum of the Sun or shooting stars to know their composition and their state; analyzes lunar stones, looks for meteorites or traces of life in space, in short he studies astronomy and all the stars of the universe.
The astronomer no longer observes by telescope, or very rarely. When they wants to shoot a star he places an electronic camera (CCD) on the telescope eyepiece and saves the image on the hard disk of a computer. In this way, several astronomers can view the image at the same time and since it is digitally recorded, they can also access it remotely via the Internet.
Some astronomers are also interested in cosmology; they seek to understand how the universe was formed and how it will evolve. They are usually either mathematicians or physicists training astronomy enthusiasts.
Astronomy being a vast field to study, astronomers are often experts in a field: some know the Sun better than Earth, others know galaxies much better than planets, and so on. It all depends on what interests you.