From the people's elected representatives at the federal, state, and local level.
In most cases, an elected School Board - a quasi government group - is elected by the people in a particular school district. I say quasi-government as technically the school board answers to no government authority other than as necessary in order to receive state and federal funds and the school board does have to follow the law of the land.
The school board draws up its own bylaws/rules of conduct, and hires a Superintendent of Schools for that school district. Generally the superintendent has a good deal of input in all school policy and curriculum, but the school board has the final say.
The Superintendent hires/appoints his/her own staff and is responsible to hire or promote Principals for each school in the district. The Principal in turn hires the teachers, coaches, office staff, and any other necessary personnel to work at the school.