How are the personal assistants for professors usually funded? As examples, the lab executive assistant at http://www.klab.caltech.edu/people.shtml or the lab administrative assistant over at http://www.gps.caltech.edu/~tapio/people.html#admins
Funding for non-research positions comes from either direct or indirect sources. 

Direct sources means writing a proposal that includes funding for personnel such as a lab technician or an administrator for a research center. In this case, the funding is obtained directly through grants. 

Most of the time, however, the funding is indirect: the salary is paid by the department, rather than an individual research group. This funding is paid for through the "overhead" charges that are included in research grants. (In some cases, such as public universities in Germany, this funding is also indirect, coming from a grant by the state or federal government given to each professorship.)