— Get fingerprinted by the NYPD.
— Get a local police background and clearance certificate.
— Submit fingerprints and a request form to the FBI for a federal criminal background check.
— Medical certification that you are free of yellow fever, cholera, black plague (and not just if you're a medievalist, either), drug addiction, and mental illness. (The guidelines do not yet say anything about being certified as being free of ebola yet.)
The average processing time from submission of all of the documentation (which includes the above, plus a whole host of more expected things, like extra passport photos, a copy of your driver's license and passport, etc.,) is 45 days. Prepare for extra delays when dealing with the federal government. For example, this is the warning at the top of the FBI page with the information and forms for requesting a copy of one's criminal history:
Realistically, this isn't going to happen in time for me to go in the spring, although we're collectively whistling into the wind at this point. It seems like it would be easier to make curriculum and staffing adjustments earlier rather than later, and I would certainly prefer not to have to waste a ton of time playing along with jumping through bureaucratic and paperwork hoops for something that's not going to happen while I'm supposed to be finishing my book manuscript, but I'm not in a position to put an end to what seems to me to be a complete folly. For now, we're working on the assumption that the university will have some kind of workaround. (Plus, as much as I was initially ambivalent about uprooting my life twice in two years, I'm disappointed that I likely shan't be going.)
In any event, the point is that I wish I'd had a lot more lead time in getting all of this together, hence the beginnings of a checklist, to be updated as I go through the process, both for myself the next time I have to do this and for any of my colleagues who are also US citizens as we start to cycle around the "global network university."