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.)
I've seen three common ways of funding staff - undoubtedly there are more.
- For staff directly related to the running of a research lab, for example senior technicians, lab managers, dedicated programmers for computational research, etc. there may be funding written into the direct salary costs of the research grants their faculty member submits. For example, many of the grants in the field I'm in have direct funding for data managers and the like for the duration of a research grant.
- If a faculty member anticipates needing a particular type of help - most often a lab technician or programmer in my experience - they may ask for their salary to be part of the faculty member's startup package for some small number of years before (hopefully) the faculty member can support them through mechanism #1.
- Other staff members, such as personal assistants, some research staff etc. are theoretically things that are supposed to be paid for by the rather sizable chunk of a grant budget that goes to indirect costs to the university. Whether or not this occurs in practice is another question all together.