Blank research courses
The Philosophical Research for credit is G83.3300-001 and the Philosophical Research for pass/fail is G83.3301-001. Use these to fill up the needed 12 credits every semester after your first year (unless you have some reason for wanting to register for three courses in semesters where you don't have to).
Registering for courses at other departments
There are two ways to take a course at another university in the New York Consortium. The first is the easy way: you take a Phil. Research here (G83.3300 - the one that counts for a grade), and then have the non-NYU instructor just email Debbie your grade at the end of the semester (of course, let Debbie know this is happening when you register).
The second way is the official consortium route: it involves going to the office of the GSAS Vice-Dean (6 Washington Square North, 2nd Floor), picking up the necessary paperwork and getting the form signed by various individuals (course instructor, Dean of non-NYU school, Director of Graduate Studies here and Vice-Dean here). You can also find the form on the GSAS webpage here. Note that when you register for the consortium course, you have to pick the same number of credits that you would get at the non-NYU university. If this is less than 4, you can pick any extra credits you need for that semester by registering for the graded version of Phil. Research.
One perk of going the second way is that the course appears on your official transcript (although even with the first way, you can still list it on your CV). Another perk is that you can usually get an ID from the non-NYU university, which makes it easier to get into the buildings, use the facilities, log onto course websites, etc. The main downside is that getting the signatures is a pain in the ass. And sometimes they try to keep first-years from participating.
Here is a list of the schools that are part of the Consortium: