By and large, amateurs coach amateur athletes in the United States. However, in other countries, a youth coach is a profession, and just like with other professions, coaches study to become coaches.
From Dr. Michael Yessis’ Secrets of Soviet Sports Fitness & Training:
The development of coaches in the Soviet Union is a scientific, well-planned undertaking. Unlike the U.S., where colleges turn out physical education teachers – some of whom become coaches without any additional spcialized training – the U.S.S.R. has developed programs designed specifically to tranform young men and women into skilled athletic instructors. Space in these programs is limited, and competition for admittance is keen. All applicants must be serious athletes themselves, and they are required to take rigorous four-day entrance exams in subjects ranging from physics and chemistryto biology and mathematics. Those who make the grade then undergo four to five years of a tough, scientifically oriented curriculum in one of the country’s physical culture institutes, which culminates with academic examinations that last for days.
The men and women who move successfully through this rigorous program become high-level coaches; those who don’t become teachers…coaching is viewed as a career that requires special training and education. Every five years, the coaches return to the physical culture institutes for a semester to receive refresher courses.