By the time an individual is hired to be the principal of a high school, he or she has already spent many years in the education system of a particular school district or in a particular state. As such, the average high school principal has a great deal of experience in the classroom, teaching students. As he or she rises up the hierarchy of high or middle school academia, the ability to administer a large institution and to demonstrate leadership abilities is required. The principal is a position of authority not only over hundreds or thousands of students, but also of teachers and support staff. He or she is expected to possess very good communication skills at both levels -- adult teachers and teenagers -- and to be experienced at resolving crises that can arise within a classroom, in the gym, or in a school yard. High school principals also must be capable of interacting on a daily basis with parents, school boards, and community organizations.
In addition to leadership and administrative skills and the ability to communicate to a broad range of individuals, a principal must be certified by the state or district in which he or she is working, the specific requirements dependent upon each individual state's laws.
In terms of education, high school principals are expected to have at least one graduate degree, preferably a doctorate in secondary education, but at a minimum a master's degree. He or she should be capable of developing a curriculum and at ensuring that all educational and athletic activities are consistent with all appropriate laws.
This answer is long after your question, but I must add to this as I have had both poor principals and good principals with one outstanding one. The outstanding one had a terrific emotional IQ, knowing just what to say to someone who needed help. She encouraged her staff to try new things, new ways of teaching, new ways of connecting with other staff, and in general, encouraged you to be the best you could be. She was always visible in the halls, available to her staff, willing to tackle any problem, and never failed to back up teachers even if later she had to explain to a teacher later that other ways could work better. She believed in doing what she asked her staff to do, including turning off the office air conditioning when the rest of the building had no air on hot days. She used the best talents of each of her staff to create a building truly supportive of the learning environment. She tackled racial issues head on with understanding of both sides. Perhaps this is a minor point, but she even came to the skateboard park to watch my students as I was the skateboard club advisor. These were not always the best of students, but she believed as I did that they were worth the time. I worked the hardest I've ever worked even though I was towards the end of my career, and gave my students the best I was capable of, which was more than I knew. As a leader, she was without a peer in all of my 37 years of teaching.