How does a faculty member get to work at two universities or more?
The situation I've seen most often is that a professor will hold a primary appointment at school A, where they have a lab and complete their research. Often for reasons related to collaboration, school B will then give the professor an appointment in a related if not identical department. If the professor also teaches a few courses at school C, they will likely be granted an adjunct position there as well.

This was my setup when I was in graduate school; I was a grad student in bioengineering at U Pitt, and I had a secondary appointment at CMU due to both lab collaborations and my being registered in a certificate program there.