The most direct path to a career in research in astronomy or astrophysics is to get a Bachelor's degree in Physics, Astronomy, or Astrophysics, and then enter into a graduate program in the field; which starts with a master's followed by a doctoral degree (Ph.D.)
Some universities offer a doctoral degree without first doing a master's degree; however, the process might be almost the same as those that start with a master's degree. This is, you might have to take some classes first and then pass an in-depth knowledge test before you are allowed to start working on your Ph.D. thesis.
If you got a bachelor's degree in one of the natural sciences like Mathematics or Chemistry, you still might be able to enter a master's or doctorate in astronomy or astrophysics. In this case, you will be required to take extra classes in physics and astronomy to give you a more solid knowledge in the field.
The best way to start on this path is to establish a good relationship with researchers at your selected university, even before you finish your bachelor's studies. Follow their recommendations on classes to take, and request their support and a recommendation to get into the graduate program (master's or Ph.D.).
Another possible path is to first work with an astronomer or astrophysicist at a research institution, learn more about this field, and build your resumé. Then you can apply for graduate studies.
The most common jobs for a researcher without a degree in astronomy or astrophysics are to be good at writing code, to have experience working with astronomical detectors, or to have previous experience supporting one or several astronomy research projects while in college.