I can't answer how most facilities handle these problems, but I can tell you how I think they should. But even this is usually inadequate. This crisis team may then make recommendations to the ER staff. However, in most cases the patient will still need vital signs, basic labs, etc. It may take several meetings over the course of months before inter-departmental issues can be ironed out.
Education is important, too, though it is often resisted.
Also see Koran et al in the August 1989 Archives of General Psychiatry. Finally, you may be interested in the November 1994 issue of Psychiatric Annals, which is devoted entirely to emergency psychiatry.