Whom do we contact at an institution for applying for a position?
The Director, the Chairperson of a particular department, or the email on the Institution's website. Different institutions are at different stages in evolving a prompt, responsive application system—meaning that you may not always hear back immediately.
If this happens, find a young scientist at the particular institution and ask whether they can give you any information about their procedures (in some places, younger faculty are only minimally involved in hiring decisions, and in others, may be able to provide informal information about the frequency of Council meetings etc which may hold up processing of an application).
Most Institutions are beginning to realize that email confirmations of applications received is a good thing to do, and hopefully this is the beginning of a change in how candidates are kept updated about the progress of their application.