I had one phone interview with the Director of my department and the Director's right hand. The majority of the conversation consisted of the Director sharing the department's culture, and the kind of person they were looking for. I was well qualified, but the priority seemed to be placed more on personality fit than career experience.
The department had a few separate positions they wanted to consider me for, so they asked me to apply to each of them online, and I did. You agree to a background check as a part of the application, but I'm not sure if one was actually carried out.
I was made an offer pretty quickly. There was a small financial barrier to leaving my then-present job, and when I asked the HR rep if they'd consider helping with that, they just increased the offer by that amount.
Once I accepted there was a health screen (TB test, which I assume is normal for hospitals) and a drug test.