How are trustees chosen? I thought that trustees of a university are leading people in the region or around the country (politicians, industrial leaders, donators, etc). I accidentally saw the Board of Trustees of Princeton University, and was surprised that one of the members is just a student from California.

It makes me wonder, how the trustees are selected? and what are the requirements for becoming a trustee?
Every university should have a documented process for choosing trustees, regents, etc. Ours are appointed by the Governor. See the link for what Princeton does. There are students on the Princeton board because a) there was a grad student among the 13 elected alumni trustees (2011 grad), and b) because there is always a graduating senior elected. Both of these kinds of alumni trustees serve for 4-year terms.