Astrophysicists study how stars, planets, galaxies, and other celestial objects work and interact with each other. Their research provides information on how the universe works. Although astrophysicists deal specifically with the physics of the universe, to study such a wide field they need to be familiar with many types of physics, including quantum mechanics, relativity, electromagnetism, and nuclear physics.
To study the universe, astrophysicists need to observe the universe, which means needing radio telescopes like the Very Large Array and space telescopes like the Hubble. Astrophysicists also do research in space, using things like the Mars Rovers and the unmanned Voyager probes. Research is also performed on manned space missions: the International Space Station researches everything from how the human body changes in low gravity to how plants are altered when grown in space. Although research like this isn't examining how the universe works, it gives us important information for longer manned missions, either to Mars, an asteroid, or beyond!
To become an astrophysicist, more education is better, and you'll most likely want to get a Ph.D. in physics. Beyond needing to study a wide range of fields within physics, you'll need a strong background in math (calculus and beyond), and a good working knowledge of computer programming (some physics courses will teach the necessary programming). Depending on your interests, geology, biology, and chemistry can all be useful as well: astro- and exobiologists, who study the possibility of life in the universe, can benefit from a background in these fields.
Astrophysics is a heavily research-based career, and astrophysicists are are primarily employed by universities, research labs (usually government-funded), and space agencies such as NASA, ESA (Europe), CSA (Canada), ROSCOSMOS (Russia), and JAXA (Japan). This is largely because the knowledge discovered by researchers is made available for free to anyone for the good of humanity instead of for profit. Occasionally, though, some private companies in fields like aerospace may hire astronomers or astrophysicists to perform research to give their company a competitive edge. Regardless of who you work for, studying astrophysics can lead to a wide variety of closely related careers: aerospace engineering (for companies like Boeing and SpaceX), designing and building scientific instruments, and advanced energy research to name just a few.
For more information on astrophysics and astrophysicists, check out NASA's Ask an Astrophysicist.
Girl Museum Inc.